Tuesday, December 11, 2012

There is no NEW math!

I have been thinking about blogging about this for a while but I wasn't sure how to put it in words.  Today two things made me decide it was time.  There was a comment that was supposed to be funny about "new math" made at our staff meeting and I read a comment on facebook criticizing the "new math".  It's time to voice my views on the subject.
First, there is no NEW math!  The rules of math have not changed!  What has changed is that there is a new CURRICULUM.  Outcomes/skills have been rearranged and a few ideas that were not in the old curriculum have been added, but NONE of these are NEW math skills!   5 + 8 is still 13!  3x + 5x is still 8x! etc.

Second, the new curriculum encourages introducing multiple strategies to solving math skills.  There is nothing wrong with this!  I read a tweet that quoted Alfie Kohn: " Irony alert:  Adults freely confess they stink at math, then object if their kids aren't taught with same methods they were."  Think about this.  It is so true.  I have parents who will freely come in at interviews and say that they can't help their son/daughter because they sucked at math.  Yet, the minute we try to show students a way that they  might understand a process that is different from teachings in the past, parents are in an uproar that they don't understand!   I can't think of another area where change is so blatantly discouraged!  We wouldn't want the medical procedures that were done in the 1930's to still be done today.  We couldn't imagine living with the technology that was used 50 years ago!  Yet, why do people fight so hard against change in education?  

My high school math teacher taught me to factor trinomials using decomposition.   This is how I taught my students for the first half of my teaching career.  Many students struggled with this skill.  The numbers could become quite large, the signs could be tricky, and an understanding of greatest common factors was necessary.  A few years ago, a colleague showed me another strategy for factoring trinomials, which we refer to as the box method.  This strategy is amazing!  Students don't need to deal with large numbers or greatest common factors.  I now show both strategies and most students choose the box method, but there are a couple who will choose decomposition.  They both have the same end result, but for some students one makes more sense than the other.  Now, instead of just reaching some students, I can reach more students because I have multiple strategies  for them.  The misconception is that they have to know ALL strategies.  No, they just need to know one of these with deep understanding. 

Another examples with finding domain of functions.  I was taught set notation in high school.  That is what I used up until 3 years ago.  I thought students struggled with domain.  I used to plan to spend two to three days just trying to explain it so all would understand.  Three years ago, when the resource came out for the new curriculum, there were alternate strategies, one of which was interval notation.  I had never seen it before and had to do a bit of reading on it to understand it myself, but when I showed it to the students something happened - they were successful with domain!   It wasn't the understanding of domain that had most puzzled, it was the notation we were using!  Set notation has symbols in it that hadn't been used a lot in previous classes.  Students weren't understanding what all the symbols meant.  Once I showed interval notation, more were being successful with domain!  In my foundations 30 class half of my students are using set notation and half are using interval notation.  If I just showed one of those methods, I may not have reached as many students as I did. 

In my grade 9 class we are currently working with polynomials.  This is the first time they see polynomials in the curriculum.  For some, they make the jump to solving symbolically with ease and others really struggle.  I've shown how to use algebra tiles for those who need a visual to help them understand.  Today, on the midterm, I had a student ask if he could use the algebra tiles to answer some questions!   Eventually I hope he is able to transition to solving symbolically as algebra tiles aren't effective with large values, but for now it is helping him to understand the process.  If I just taught "traditionally" as the naysayers of the new curriculum want, then this student would still be unsuccessful with basic polynomial operations because I would only be teaching the symbolic strategy.  He wouldn't have a chance to develop an understanding.  I believe he will eventually move from visual to symbolic the more he practices with algebra tiles.

Another focus of the new curriculum is for students to explore and develop their own understanding of the math "rules".  For example, in the past we simply told students that any power with exponent of 0 was equal to 1.  "Just memorize this."  I have a math major from university and I never knew why this was until the new curriculum came out and I completed an explore in the resource to discover this!   I think about this and am thankful that I was good at memorization!  Math came easy to me because I was able to memorize all of these processes and rules.  However, for those who struggled in math we have to ask "why".  And I believe the answer is that the curriculum never tried to reach all learners.  You were taught one strategy (in most cases - some teachers did expand a bit) and it was sink or swim!   Now my grade 9's do an explore where they see the pattern that leads to powers with exponent zero being equal to 1.  Ultimately we still state the rule, and some students will just memorize this rule, but there are many more that will now have the understanding of why and will be able to remember this rule in the future.   If they are able to develop the rule instead of being told the rule, their understanding will be deeper and they will be more likely to recall this information later on.

I could go on and on where showing multiple strategies and inquiry has reached more students than just picking one for all.  Just like one shoe size doesn't fit all, neither does one strategy reach all learners!

I do understand that some students get confused when presented multiple strategies.  What I will often do, is after showing one strategy, I will tell students who struggle with seeing more than one way to cover their ears if they understood the first method.   If they didn't understand the first method then they might want to watch the second in case it makes more sense!

Another criticism of the new curriculum is that parents/society don't feel that students are learning the basics.  The basics are STILL taught.  Students STILL learn to add, subtract, mulitply and divide.  There are some strategies for these skills that may be new to some people.  It is not about rote memorization anymore.  Let's be real - what percentage of adults do you actually think could recite their multiplication tables without any thought?  Not many.  Most people have either forgotten some of the products or have developed a strategy to recall the product quickly.  These are strategies we want our students to have.  At some point, fluency is important, but if they have a strategy that will help them retrieve the answer quickly then that is what they need.  My other issue is that why do parents feel it is only up to teachers to drill these facts into the students.  Why can't parents take initiative and work on these basic skills at home?  My daughter is in grade 2 and my son is 4 and we do basic math skills regularly at home.  My daughter has a poster with multiplication facts on her wall.  Yesterday I walked into my daughter's bedroom and my son was looking at the poster, giving her two numbers and she had to say the answer.  They will both learn their multiplication facts by practicing together at home.  My daughter comes home each day with a "green bag book" and is expected to read for at least 15 minutes daily.  Why can't we also do 15 minutes of math facts?  This will help with recall of basic skills.  If parents spent this time with their children so many of the math skills taught in class would be understood a lot quicker.   I get that parents may not be able to help with some of the more complex processes, but doing basic math fact questions daily should be easily handled by most.  I don't want my daughter's math teacher to be spending too much time worrying about drill and practice on basic math skills - I want her to be teaching strategies and understanding of number systems and patterns in math and I will look after the basic recall of facts.

I do think that some of the negative views have been fostered due to a poor rolling out of the curriculum.  I feel for elementary/middle years teachers who were given multiple new curriculums to learn all at once and were told that there were new assessment strategies that needed to me implemented as well, yet there was no extra time given to plan for these, to learn about these, and to collaborate with others.  A teacher who all along has only known one strategy  and has no time to learn a new strategy is likely going to struggle the first couple of times through.  Professional development is crucial to teach teachers how to use manipulatives and various stratgies that are not familiar to them.  Also, there was not a lot of guidance from the Ministry on what the purpose of multiple strategies are and many teachers thought that ALL had to be taught and understood.  In reality, they are in the resource to assist in reaching all learners, but students, in most cases, only need to be literate in one effective strategy.  Once teachers have the chance to learn about the purpose and learn about the strategies, it will spill over into the classroom and things will run a lot smoother.  We tell our students that practice makes perfect and it is the same for teachers!  The more I teach something the more I feel comfortable with it, the more I feel comfortable with multiple strategies, the more I find out where students struggle and the better I am prepared to assist all learners in developing a deep understanding of the skill.

Ultimately, my advice to parents is that you don't be afraid of the math that you see.  Embrace the new strategies and be willing to learn alongside your son/daughter.  Challenge your son/daughter to teach you this new strategy - if they can successfully teach you then they have a deep understanding of the skill/process!   If you get to the point where you or your son/daughter is not able to complete the work at home, don't be afraid to seek help from the teacher.  Ask the teacher to explain the strategy to you.  Ask them to send an email, a note, a photocopy of explanation from resource.  At home, work on basic math facts instead.  You can never go wrong by having a strong skill set in that area.  Send a note back to the teacher that you worked on the problems but were unsuccessful and will require more assistance.  Please do not play into a struggling student's hand by agreeing with them that "this sucks" or "this is stupid" or "I don't need this anyways".  Tell them that it is important to try hard and do your best and it is okay to ask for help.  Model this behaviour for them!

Embrace the new curriculum, embrace the changes occuring, and please realize that there is NO NEW MATH!!!!!

Thursday, December 6, 2012

Growth Mind Set

Today in our Learning Leader's meeting we talked about fixed mind set vs growth mind set.  It was an interesting discussion.  I know I used to have a fixed mind set.  I believed that people/students fit into different categories - ie. A students, B students, great athlete, good athlete, poor athlete, etc.   Now I believe I have shifted towards a growth mind set.  I believe everyone can improve.  We don't all improve at the same rate, and I don't believe that we will all get to the same level in our lifespan, but I do 100% believe that everyone can improve at what they want to.

I think that in our traditional education system we set students up to have a fixed mind set.  They were either good, average or poor at math.  We did this because we taught a chapter, tested it, gave the evaluation to the student, and that was the end of it, we moved on to the next chapter.  Typically students stayed in a particular "grade" range from test to test.  We didn't talk a whole lot (or at least I didn't) about learning from the "test" and improving our knowledge.

What really changed my belief was moving to the 4 point rubric.   Here it is easy to talk about growth and have a growth mind set.  The same scale is used so we can discuss the growth of learning.  My first  success story with this was in the first year of using the rubric.  I had a student with a fixed mind set - she hated math and sucked at it and always failed, so why try.  We've all had those students.  She had a fixed mind set as she didn't believe she could learn and improve.  As I started to think more about growth I simply pointed out to her how proud I was with an assessment result because she had shown improvement since we began that outcome.  She thought about that and her mind shifted.   Once I had pointed out that she had gone from not knowing, to learning a little, to having a basic understanding of the outcome, she started to believe that she could learn.  Her attitude changed as she shifted to a growth mind set and the results for her in the class were a success.

I love that with a growth mind set we are not comparing to one another (ranking), which is what a fixed mind set does.  I think a good example of this is when you take your child to the doctor for their annual visit and their height and weight are charted on a percentile chart.  Yes, your child is "ranked" in a percentile according to others, but that is not what my doctor focused on.  He didn't care if I they were at the 70th percentile or the 5th.  What he focused on was that they followed the growth pattern fairly close and remained about the same.  A huge drop or increase was cause for concern.  I try to get my students to see this as well.  I don't want them to compare how they are doing to anyone else, I want them to look at whether they are improving on their learning.  When a parent asks me what a good "score" is on the rubric, I tell them it depends on the student.  What is more important is whether the student is showing growth and if they are then learning is happening even if it is at a slower/faster pace than someone else.

I think that it is also important with this measurement tool (4 point rubric) that reflecting on learning is occurring.  I know I am working on being consistent with this.  If all you do is return an assessment with a "score" on it, and there is no follow up, then it can lead to fixed mind sets again.  If you return the assessment and have the students reflect on where they are at in their learning, what they have been successful with, what they still need to learn, and whether they have shown improvement, then you are fostering a growth mind set.

What I have found really interesting through this journey is that those who are most opposed to the 4 point rubrics are either students or parents of students who would be deemed "upper" end students if we ranked the students.  Today's conversation lead me to believe these are of a fixed mind set and need the validation of the high marks and ranking.  Scholarships and University entrance often enter the conversation.  Really, University entrance is not an issue - students will be provided with the necessary University required "grade".  And really, what percentage of students are we talking about here?  Not a whole lot!   This system can reach ALL students.  Sometimes I wonder if this group is worried about others "catching" them and then they are not alone at the top.  I really do think that this validation is necessary for them.  And that is something that we need to change.  I really don't hear any of the "lower" or "middle" ranked students/parents complaining about this once they have listened to the purpose of this system (initially they might have a negative view until the purpose is explained).    They see the benefits of being allowed to improve and being encouraged to learn.

I love how the 4 point system that we have implemented complements a growth mind set.  I know I have to improve how I use the system in my classes so students see the benefits of believing that they can learn and not being satisfied with where they are at.  This is all about being life long learners.  We should all try to improve ourselves daily!

On another note, I watched the following video this evening (click here) and would like to thank the "first follower" who joined in with trying rubrics four years ago, and then the next and the next.  Without you guys, we would not be where we are today!

Wednesday, November 21, 2012

Mini Conferences 2

A couple of posts back I blogged about mini conferencing after an assessment.  I have begun to do this regularly.  I really like it.  It serves multiple purposes.

First it allows me to check understanding that was incomplete on the assessment yet I feel the student actually does understand (based on formative results in the classroom).  Many times I don't score the assessment until after I have had a conversation with the student.  I want to be sure their score accurately reflects what they understand at that particular time.

Second, it allows the student and I to touch base one on one.  I try to do this with all students as often as possible, but realistically some students are more vocal with asking for help and some shy away from it.  In these conferences they have to speak to me!  I am able to probe into their thought process in order to get a better feel for where they are understanding the outcome.

Third, I am able to discuss with the student their areas of weakness (and strengths).  We can go through the questions they had errors on and discuss whether it was a simple error or something they need more help on.  One on one the student is more focused than if I simply went through the answers with the whole class.  Many times through the conversation  I have realized the error they made was not the error I assumed they made so it is easier to correct the misunderstanding.

Fourth, I am able to score the assessment AND give a comment AND have the comment looked at by the student.  Research shows (Wiliam) that if both a comment and a grade are given the student does not look at the comment.  Learning does not take place.  When they conference with me we discuss the comment!   I do have some other ideas that I would like to try down the road where the student only receives a comment, yet I can score the assessment in my gradebook, but that is for another discussion/post at a later date!

This whole process can usually be completed within 20-30 minutes of a class.  Instead of giving the assessment back at the beginning of a class, I now "teach" the next lesson and then while the students are practicing, I call them up one at a time and we have our conference.  Some are really quick as some students are at level 3 or 4, so not a lot of misconceptions.  Really when a person looks deeply at the assessment it is typically one or two misunderstandings and when the student is right in front of you it doesn't take long to correct these.  If I do have a student who is really struggling we can set another time for them to meet with me for extra help.

I have really liked this process so much that one time recently the follow up lesson included an exploration so there was no time for practice, so I told the students they had to wait an extra day for their assessment to be returned!   I wouldn't stretch the wait time out more than a day as it is important for the students to see what they have done, but one day isn't going to make a huge difference and the value of the conference outweighs the extra day!

Thursday, October 25, 2012

PLC Update

Our PLC group met again this morning to touch base and see how things have been going.  We started out with another video clip from a classroom observation.  One of our members has begun using the red/green cups (a strategy found in Dylan Wiliam's book Embedded Formative Assessment).  We were able to get a good video of a lesson where these were used well and I edited it to just under 3 minutes.  During this time we saw how during one example, a large amount of the students changed their cups to red, so the teacher went through the example as a class discussion.  Two other times individual students changed their cups to red, so the teacher dealt with them individually.  During our meeting the teacher reflected on how things have been going.  She said she was nervous to try this, as it seems so elementary, and she has grade 10 and 12 students.  However she said they are liking it and asking for them.  She said she hasn't yet asked them why they like it.  We have discussed possibly furthering our video to include video clips of the students sharing their thoughts on the use of the cups.

Two other teachers shared what they observed during a classroom observation.  One noticed a difference in questioning techniques, and the other on organization of board space during the lesson.

We left the meeting with a goal of within one month each teacher needs to make a point of observing someone else and being observed.

Tuesday, October 9, 2012

A Day With Dylan Wiliam

First off, I'd like to thank our division for investing money in teacher's professional development.

Second, I'd like to thank my school's PD committee for thinking outside the box.  Let me explain.  Two years ago, 5 teachers from our school attended a conference in Scottsdale on Standards and Assessment.  At this conference we heard Dylan Wiliam speak (bio here).  I know I took away a lot from listening to him and I'm pretty sure the others did too.  The past couple of years we have begun to implement some of the strategies he talked about regarding formative assessment.  Last spring, our admin asked if we thought he'd be worth bringing in.  YES!   They thought that instead of sending a limited number of teachers to a conference where you hear a person for a short period of time, they would bring the person to us!   What an amazing opportunity!  As a result, the PLC group I belong to decided we would do a book study of his Embedded Formative Assessment this year.  I blogged about our goals here.

Today, 40 of our math and science teachers got to spend our PLC day with Dylan Wiliam.  Today was a great day.  I thoroughly enjoy listening to him speak.  He is knowledgeable, witty, and has stories to back up what he is saying.  I could write an essay on what I learned today.  Instead I will highlight a few points.

On Education Today
1)  We are preparing students today for a world that we know very little about.  Jobs are changing at a rapid pace and we need to teach kids how to become thinkers and teach them the skill of wanting to learn.
2) The solution is not in spending more money to change the physical makeup of the classroom, add technology, etc.
3)  Teaching is a HARD job!  And because of this we need to help teachers become better teachers.  He says a lifetime is not enough time to master teaching.  We have a hard job and will always encounter failure.  We simply need to keep learning in order to become more effective.  It is important to note that we are not bad teachers, we all go to work doing the best that we can, but we need to help each other become better.  It makes sense - why would I want to be the same teacher I was ten years ago?  I'd like to think I've become better and that I can still get better yet!

On Formative Assessment/Feedback
1)  The closer the formative assessment is to instruction, the bigger the effect on learning (ie.  if you collect your evidence and make immediate decisions based on this evidence for the students you collected the evidence from, it will have a greater impact on their learning)
2)  Feedback should be forward looking and not looking back.  It needs to inform the learner of what needs to be done to improve.
3)  Regular checks need to occur
4) Getting feedback right is hard.  Feedback can have a negative effect on learning when done incorrectly, so it is important to know your students so you can be sure they are getting the correct balance.  They need to be challenged, but only so that they feel it is attainable and not out of their reach.
5) The only good feedback is feedback which is acted upon.  You need to provide time in class for students to reflect on this feedback.

On questioning
1) You need to know a purpose to your questions.  You want questions that promote thinking.  It's not about closed vs open, but low level vs high level.
2) Love his "pose, pause, pounce, bounce" strategy - the teacher poses the question, pauses for students to think about it (he said a study showed the average wait time was 0.9 seconds!!!!  Need to give time to think), pounces on a RANDOM student (as opposed to a "volunteer"), and then bounces the answer to another RANDOM student.
3)  Discussion questions - a multiple choice question where a student might select any one of the answers and then you need to discuss with the class as to what their reasoning is behind their thinking.
4) Diagnosis questions (Hinge questions)- a quick question to make sure everyone is understanding what you want them to understand.  This question must be a GOOD question - there shouldn't be a way to get a correct answer with incorrect thinking.  These questions need to be planned ahead of time and critiqued by other teachers.  Idea - have a group of three work on these questions and then give them to another group of teachers to see if they can find a way a student might get a correct answer with incorrect thinking.  If they can then you need to find a different diagnosis question.    He says that with these questions you must be able to collect and interpret the responses from all students in 30 seconds.

On Strategies For the Teacher in The Classroom
Dylan Wiliam provided a large number of formative strategies that can be used in the classroom.  This is what our PLC is working on.  It is important to not overload yourself with these and that you make individual choices with which you might try.  Although all sound very good, there are a couple that stood out to me and they will be the first ones I get to as I decide to try new things.
1)  Structured Interaction - Teach students to pose/develop/ask questions during a lesson.  This will increase engagement.  How I see it working for me is that I would tell the students that as the lesson is occurring they need to be thinking of questions they might want to ask me.  Some questions need to be dealt with immediately, but some can wait until the end of the lesson.  Instead of me asking "does anyone have any questions" I would pull three popsicle sticks (random selection) and ask them for the question they constructed during the lesson.  This is intended to have the students thinking about what is going on and making them active participants in the lesson.  I would like to try this at some point!
2)  Self Reflection with red/yellow/green mixed with creating test questions.  I would like to have students, on a review day, first pre-assess themselves with each skill that is in our rubric as to whether they feel they are red (no clue), yellow (sort of understand) or green (good to go).  Then their review would consist of creating test questions complete with solutions for each of those skills, starting with the skills they are red in.  At the end of the lesson I would have them assess themselves again to see if they feel they have improved their learning.  I hope to try this at some point.
3) Mini Whiteboards - I went out today after the workshop and bought page protectors and dry erase markers so I can start using an all student response system this week!

There was so much more that I got out of the day, but it is too much to write about.  Those were the key points that I took away from the day.  The last thing that really stood out is that he said improving our practice involves changing habits, not adding knowledge and that's why it's hard.  The hardest part is not getting new ideas into people's heads but it's getting the old ones out!

There are two videos online from a project he was part of where they followed a classroom through many of these changes.  It was good to watch how everything wasn't instant success, but the teachers and students kept plugging away and the end result was very successful.  You can watch the videos here and here.  They are both about 1 hour long, but very worthwhile to watch.

Once again, I thank our division and our school PD committee for providing us with this amazing opportunity.

Friday, October 5, 2012

Mini Conferences

Over the past few years as I've become more aware of the necessity to improve my teaching strategies, I've read about the importance of having individual conferences regularly with your students.  I've struggled with finding the time to do this, especially in high school where you only see the students for 1 hour a day and typically have between 20 and 35 students in a class.  Over the last year I've managed to find a starting point.  Today I did this with my grade 9's and found it very successful.  Here is what I do.

Yesterday the students wrote an assessment.  My weekly assessment's are not summative in nature - I will record their level of understanding to collect evidence of learning, but we are to learn from the results, which really makes them formative in nature and we will do additional assessments based on what we get from the assessment.  But the kicker is that I have to make sure that the feedback the students are getting from these is effective and will move learning forward.  I'm starting to figure this out.  I haven't mastered it by any means, but I am getting better.   What I did today was taught the next lesson and then while the student's were working on their practice, I called the students up one at a time.  We looked through their assessment.  Some students I gave a second opportunity on a particular question.  Some had not answered the question in it's entirety so I gave them an opportunity to complete it so I could really gage their level of understanding.  Others had made one mistake at a particular level so I allowed them a second chance to see if they just had a mental block yesterday.  Then for those who had questions incorrect, we discussed these.  I asked how they had arrived at their answer so that I wasn't assuming an incorrect thought and then we corrected that misconception.  It went really well.  I had enough time with the students and they got 1 on 1 feedback.  I then had them complete their learning log as a reflection on the assessment.  The three questions I asked were:  What was one thing you were proud of; What was one thing you were disappointed in; and What follow up needs to be done to improve?   I was impressed with their reflections.  I had a student who was proud that she tried on the exam, but knew that her follow up was to practice more.  I had a student who, the day before the assessment wrote that he was struggling with this material, get a 2.5 and write he was proud of how well he had done!   I had a student who had 3.5, write for his follow up that he needs to spend more time reviewing his assessment before handing it in.   These are good reflections and ones that need to be followed up on after the next assessment to see if they made those changes!

I am happy with how it went and plan on continuing this process.  My next goal would be to find time to do this before the assessment as well!  

Wednesday, September 26, 2012

Monty Hall Problem

In my Foundations 30 class we started our probability outcome last week.  As a "hook" to the outcome, we spent a day exploring the Monty Hall Problem.  For those of you who grew up watching Let's Make A Deal, you will know who Monty Hall is!  For those of you who don't, simply google Monty Hall Problem.  It is a mathematical paradox that has had many people talking about it.  Most of my students did not know about this show or who Monty Hall is.  I explained to them a bit about the show and we watched a short clip on youtube about the show so they had some background.  I then explained to them the finale of each show - three doors presented to a contestant, 2 of which had goats and one which had a prize - typically a car.  The contestant had to pick one door, Monty Hall then opened one of the other doors where he knew there was a goat, and then asked the contestant if they wanted to stay with their original choice or switch to the other door.  I left it at that and gave the students a few minutes to discuss whether they would stick or switch and why.   As I walked around and listened to the conversations I was impressed at what they were thinking.  Some were saying they would stay because that was their gut feeling and they would regret if it was in their original pick, others said they would stay because you had a 50-50 chance anyways, and a few said they would switch because they would increase their chances.  It was also interesting because the level of engagement was higher than normal and I had a couple of students googling the problem on their phones!   After a few minutes I had some students share their thoughts.  It was interesting as how most felt it was a 50-50 chance and the few who thought the chances would increase were shy to share why since they weren't the majority!   I didn't give anything away, just listened and asked why they felt the way they did.   I then shared how we had done this as a group of teachers last year and that we were also split on our opinions.  We then watched a mythbusters youtube video on this problem.  It explained and showed that a person actually doubles their chances of winning if they switch.  That surprised many of the students.  This was a good hook for probability.

The next day was when I realized how engaged some students were and how great of a hook it was.  I had a student who struggles with math, doesn't have regular attendance and often comes late say to me "you know I hate math but that problem we did yesterday...I couldn't stop thinking about it and I hated that... but I still think I'm right with 50-50 and it bugged me and was all I thought about."  AWESOME!!!!!  When you can get a student who openly hates math to THINK about a math problem, you know you have engaged them!   I only wish I had a bag of magic tricks to do this every day!  Maybe by the time I retire I will have this bag of tricks!  For now I'll take it when I can and be satisfied that I was able to succeed even once for now!  And not that I'll stop looking, as I'm always looking, but I am happy for the feedback that I received!

Wednesday, September 19, 2012

What I Learned From Observing A Colleague

I mentioned in a previous post (here) that one of our PLC goals was to observe and learn from other members of the group.  Yesterday I did my first observation of a colleague.  I even managed to convince the person to let me video tape their lesson.  She agreed as she said she is always telling her students to get comfortable with being uncomfortable, so she thought she should be able to step out of her comfort zone too!  The agreement was that she would view anything I edited first before I showed it to the rest of the group.

I feel it went really well.  My initial plan was to observe her use of popsicle sticks for questioning random students.  I wanted to see how that was working for here.  However, I learned three things during my time in her class.  We both teach the same course and I had just taught the same lesson the previous day.  She began her lesson a little differently from what I did.  She did a word association for two new terms.  I really liked the idea and will consider doing something similar as I move forward.  I liked that the students had some good ideas and were okay with sharing them. That was my first learning experience of the class.

 Second learning experience:  I did get to see how she incorporated the use of popsicle sticks to ask questions and I will likely be starting this with my grade 9's once I find time to go and buy the sticks!!!!   I have a few "blurters" in that group and the same ones are always putting up their hands.  I generally try to stop the "blurting" and typically don't allow a person to answer once they already have until we have been through the entire class, but I think popsicle sticks will assist with controlling this.  I could tell that her students are already used to this process.  When called upon they were ready with an answer.  She was sure to say that they needed to be prepared with an answer, but it was okay to be wrong.  I believe that is very important.  I try to instill that in my students as well.  It is important to be thinking about the question and it is okay to be wrong - that is how we learn!  I liked that when she was doing her word association, the third student she asked said all of their answers had already been used, so instead of letting the student off the hook, she asked the student for a real life example.    There were some great questioning techniques that I had an opportunity to observe.

My third learning experience was quite a surprise to me!  My colleague was working on Venn Diagrams with the group.  This is a relatively new topic for me.  I did have two strategies for working through problems with intersections, but I learned a third strategy from a student!  It is always nice to find multiple strategies to solve problems, and always exciting when you can learn from the students.

I had video taped the entire lesson, and was able to edit a 3 1/2 minute video for our PLC group to watch.  I think the video captures three effective teaching strategies.  1)  Word association - we need to let students develop and explore terminology first, before it is defined mathematically.   2)  Random questioning - this keeps all students engaged.  If a student knows that the teacher will only call on those students who put up their hands or blurt out the answer, it is easy to disengage.   If they don't know whether they'll be called on, it is important to be following along.   3)  When a student doesn't feel they have an answer to contribute, you don't let them off the hook.  You also don't leave them out to dry.  You ask the question another way or try to scaffold the question so they can answer.  This is how they will learn.

I was really happy that I could get all three of these ideas in a short video clip.  We will be watching this at our next PLC meeting so we can reflect on those practices.  Hopefully one day we will all be comfortable enough to share these video clips outside of our PLC groups.  When this colleague and I were discussing this, we talked about how we as teachers, need exemplars.  It is one thing to read about a strategy, or listen to a colleague talk about it, but it is another thing to view a strategy being done effectively.  It is funny how we always talk about needing exemplars for our students so they know what is needed to show deep understanding, yet we don't think about that for ourselves.  We need to start thinking about ourselves.  If we want to improve, what is the best method to move us forward?  I believe part of it is learning from others and that involves observing them.  I look forward to going into another colleague's classroom at some point.  I am hoping they will also be open to my video taping so that everyone can learn from the experience.  I went into this one hoping to learn about one idea, and came away with three ideas.  I'd call that a success!

Tuesday, September 11, 2012


I was introduced to Dan Meyer's 101 questions (click here) last spring and have begun to use them in my classes.  I use them as an introduction to an outcome, or even just an activity during a class.  It is amazing how teenagers (grades 9 - 12) filter their questions in front of their peers.  They don't want to appear "stupid" or "silly".  I have been trying to teach them that we ALL have thoughts and questions when we see something and they are not stupid or silly.  I will ask random students to tell me the first question that came to their mind when they saw the picture.  It can be like pulling teeth!  I'll get "I don't know".  I tell them that they must have a question when they look at the picture and they'll finally say something.  Usually I'll get a couple questions and then the next person will say they had the same question as someone else.  Doubtful...  I do find the grade 9 students are more open than the grade 12 students.  I ask my students if they have younger siblings or relatives and if those youngsters drive them crazy with their "why" or "what is that" questions!  I tell them that I have a 4 and 7 year old and they are ALWAYS asking me "why is that...", "why can't I...", "what is that..." etc.  I get to the point where I tell them that is enough questions!   However, I feel bad about this as I feel we, as adults, stop kids from having thoughts and an imagination.  I tell my high school students that I want them to stop filtering their questions and just ASK the question that is in their head.  By the end of the year last year the students were getting pretty good at this.

And now I've started over.  I have new classes and new students and I feel like I'm pulling teeth again with them!  The first go at this a week ago was not overly successful.  I think I had three questions from the class for a picture.  Tomorrow I will be doing two new pictures.  I decided tonight to ask my 4 and 7 year old what questions they have when they saw the pictures.  They were super excited to help me out when I told them I was going to show them grade 12 math (even though it's not directly grade 12 content)! 

Here is the first picture I showed them (we are starting set theory tomorrow with venn diagrams as a big part of the learning).   The link can be found here
Right away my 7 year old says "we're doing these in math (she's in grade 2) and this is sorting".  I couldn't believe it!  My grade 12's better have a clue!!!! Haha!  She then went on to say she knows why the middle guy is there "because he has a keyboard which is the yellow and he holds his instrument which is the blue"  Unbelievable!  Anyways I asked my kids to ask me questions about this diagram.  Here is what they came up with (even my 4 year old had questions!):
Why is there only one animal in the yellow?
Why different groups?
Why are there different animals?
Why are there three animals?
Why is there one animal in each color?
What is this sorting?

My kids had so much fun with this.  We did two more pictures and they wanted to keep going!  I told them we would do some more another day. Once again I got tired of their questions :(  Why do we do this as parents and teachers?????

Tomorrow I am going to see what my grade 12's come up with and then I'm going to share the questions my kids had with them.  I will remind them that they too, were once full of questions and that those questions are still in them.  I want them to become comfortable asking the questions.  We'll see if they can come up with more questions than my kids did!

Monday, September 10, 2012

Our PLC Group

In our school division we are very fortunate to still have PLC days set aside throughout the year.  I know in some divisions these have been reduced or taken away.  In the past few years I have found these days to be very useful.  Our school has been working on building effective PLC groups.  I am very excited about our group this year.  We have chosen two goals to work on.  One of them comes from Dylan Wiliam and his book Embedded Formative Assessment.  We have all read this book.  Dylan Wiliam is coming to our school for our second PLC day this year!

The first goal is that we are all going to work on improving our formative assessment strategies in our classroom to impact student learning.  We have all read the book and decided to choose one or two new strategies to try.  We decided that it was important to limit ourselves to one or two new things so that we are able to follow through with them.  Once they become routine then we can add in some more.  There were so many great ideas in the book that it was hard to choose only one or two!  

When we had our first meeting, we all shared what we were going to try.  It was neat to see how different strategies stuck out to different members.  The majority of our group either already does or is going to start incorporating entrance slips into their daily routine.  I blogged about these here.   Those of us that already do this feel strongly about how it impacts student learning so most other members decided it would be a good one to try.  A large number of our group also decided that they were going to use tracking student growth (which I blogged about here).  After that, it was interesting to see what others were going to try.  One person is trying to improve their randomness of questioning by using popsicle sticks with students names.  Another is going to try the red/green disks for a quick view of how students are doing during the lesson.  Another teacher is going to have students do self reflection using a rubric of understanding.  I am going to try learning logs to have students self reflect on their learning.  These were all ideas from Dylan Wiliam's book.  There are many more that I would like to try, but I need to focus on small parts at a time!   We will be reflecting on these practices at our monthly meetings.

Our second goal is to improve communication with parents, students, the community and each other.  We will be sending out group emails to parents on a regular basis.  We want them to feel comfortable talking to us.  We want them to know what is going on in our classroom.   We plan on creating some videos that explain our math pathways, assessment policies, etc.  We will share these with the parents and students.  We are also going to step outside our comfort zone and start to learn from each other.  Our goal is to observe at least one other teacher's lesson in the next three months.  This is uncomfortable for some as they are nervous when others are observing.  We are not doing this to be critical.  We want to learn from each other!  Each of us has strengths that should be shared with others.

I am looking forward to improving my teaching and hopefully that will impact student learning.  I believe this PLC group will allow me to do this.

Sunday, September 2, 2012

The Phrase I Dislike the Most

I will have some really good conversations with parents about how their son/daughter is doing in math during the course of a semester.  However, there is one phrase that I hear at least once a semester.... and I REALLY dislike hearing it.   It is when a parents says "I was never good at math either..."   Do people really think that math genes are hereditary?   You don't often hear people tell someone that their child can't read because "I don't know how to read either."   Why do people feel it is acceptable to say that they are bad at math?   I think that by saying that you are poor at math you have now told your child that it is okay that they are struggling with math.  A more positive approach would be to say that "I too struggled with math, but I know it is important to work really hard, ask for help, and not give up as these are important skills to have."  I don't like it when a parents sloughs off their child's struggles because they couldn't do it either.  That is not acceptable!  

I read a really good blog post about a positive way parents can approach math with their children.  You can read it here.   I really like the suggestion to have parents ask their child to tutor them in math.  I think that this would be a fabulous way to get to the deep understanding of an outcome.  If a student can explain the outcome and teach someone else they have a solid understanding of what is going on.

I would like to work on communicating with parents the importance of hard work and persistence.  I understand that some parts are going to be difficult, and everyone does not learn at the same PACE, but it doesn't mean you CAN'T ever learn it!   Let's not allow students an out to learning!

Thursday, August 23, 2012

What an Assessment Looks Like for SBG

We are on week two of the math blogger initiative and one of the prompts this week is to share one worksheet/assessment/etc.  Since my last post was on how we grade using a rubric, and I referenced how we format our assessments I thought this would be a good time to share one.  Obviously I don't want to post an exact assessment as my students may read this!  Instead I have posted a review worksheet, which is virtually the same as the exam.  The level 2 and 3 questions will simply have different numbers/values.  I tell my students that level 4 can be anything related to the outcome, so these two questions are simply sample level 4 questions. 

N9.1A Reassessment Binder Review

You will notice that we include the rubric on the assessment.  We feel this is important as the students are then asked to reflect on their learning when the assessment is returned.    The rubric will help them to see what they know and what they still need to work on. 

We have also decided to be transparent in the level of each question.  What this does is ease the student into the assessment.  If you put a difficult question at the start (which I have done in the past!) you may increase the anxiety of students and some may not be able to continue even though there will be questions they know.  Some people might worry that students will only answer the level 2 and then quit.  This happens very rarely in my experience.  Because we focus on learning and improving, most want to do as well as they can and they realize there is no punishment in simply trying.  This format also makes it really easy to score!  We are currently working on re-formatting all of our assessments this way.

Monday, August 20, 2012

Grading with a Rubric

In an earlier post (here) I talked about the 4 point rubric that we use.  Now that we have the rubric,  we need to make sure everyone understands how to grade with it!  What we discovered early on is that there were some misunderstanding to this process and some were still grading each question /4 and then finding an average of all of the scores.  This is not the way we want to be using the rubric.  In fact, one thing that should be pointed out is that at no point do you ever want to see a  #/4 on an assessment.  Mathematically this can be confusing, as students will convert to a percent and the rubric is not about a fraction/percent "grade" but a level of understanding.

In Robert Marzano's book Formative Assessment and Standards Based Grading he spends a whole chapter (3) talking about this scale and showing how to score with it.  He talks about organizing assessments into three sections - one for score 2.0 content, one for score 3.0 content and one for score 4.0 content.  (Page 46)   We now do this on all of our assessments.  The students are well aware of where each question fits on the level of understanding rubric.  Marzano then goes on to say that "to score this assessment, the teacher would look at the pattern of responses across the three sections.  If a student correctly answered all items on the test, she would receive a score of 4.0.  If she answered all items correctly in section A (level 2) and B (level 3) but not C (level 4), she would receive a score of 3.0.  If she answered all of the items correctly to section A but not B and C, she would receive a score of 2.0.  If she could answer no items correctly on her own but could answer some items correctly with help from the teacher, she would receive a score of 1.0."  (Page 46)  This is exactly how we grade with our rubrics.  The challenge lies with those students who have some questions correct in a level but not all.  This is where our half points come in to play.

This has been difficult for some students to understand.  They might have the same quantity of questions correct, but score different from a peer and wonder why.  It has taken a lot of teaching to have them understand that they need to read the rubric to see where their level of understanding is consistent.  I have given back assessments to my students that does not have a score on it.  I have corrected the assessments and recorded in my gradebook their score, but have not written it on their papers.  I ask them to go through their assessment, read the rubric and score their assessment.  I then take them back in to see what they think.  Most students are bang on.  The ones that aren't we then have a discussion.  Some have even convinced me that they deserve the score they gave.  These conversations show me that their level of understanding is maybe higher than I thought.  I would like to do more of this with my students this year.

A couple of my colleagues and I created a couple of short videos to help others understand how to grade with a rubric.  These were done a couple years ago and the look of our assessments have changed, and the rubric has changed but the idea of how to grade has remained the same.  The videos are here and here.

This year our math department will meet on a regular basis to do common grading.  I believe this is also important to make sure we are all interpreting the rubric consistently and to see if any need tweeking because we are too far apart in our interpretations.

Wednesday, August 15, 2012

Learning Logs

I have signed up to be a part of the math blogging initiative and have been given my first "assignment". I am looking forward to this initiative and learning from other teachers!

One of the choices for our assignment was to blog about one or two specific things that we plan on doing differently this year.  One change I am planning on implementing with my math 9's is to incorporate learning logs into the classroom.  I feel that I have managed to find an opener for class (My favorite formative activity) that works well, but I don't have a good closer.  Typically the students are completing practice until the bell goes.  

I have been reading Embedded Formative Assessment by Dylan Wiliam (a great read by the way) and found the idea of a learning log (page 157).  A learning log is a way to get students to reflect on their learning.  I also think it will help me improve my skills as a teacher by reading what works well and what doesn't for the students.   My goal is to implement this with my math 9 class in semester 1.  My math 9's have always been my guinea pigs.  They are willing to try new things and we have more flexibility with time to work out kinks.   Assuming it goes well I will implement it with all of my classes in semester 2.

My students have duo-tangs that are left in the classroom where they keep their continual progress reports (click here to see these), and assessments.  I am also going to include sheets for their learning log in these.  That way if they stay in the classroom I can sit down and read through them when I have time (my goal is once a week!).  The suggestion in the book is that you provide them with the following prompts and the students are to choose no more than three to respond to that day.  I am not sure if I will give the complete list or if I will choose one or two each day for the students to respond to.  I am also not sure if I will ask them to choose only one a day or allow up to three.  I plan on doing this with 5 minutes left in class.  Any suggestions on how to proceed would be appreciated!

The prompts suggested in the book are:
Today I learned...
I was surprised by...
The most useful thing I will take from this lesson is...
I was interested in...
What I liked most about this lesson was...
One thing I'm not sure about is...
The main thing I want to find out more about is...
After this session I feel...
I might have gotten more from this lesson if...

I really liked this idea when I read about it.  I hope to have it become part of our daily classroom routine.

Sunday, August 12, 2012


When making a shift to learning for all, one of the discussions/debates is centered around whether or not to allow "redos".  This is a tough one for a lot of people.  Four or five years ago I didn't believe in redos.  I felt that if the student worked through the unit, did the assignments, asked for help, completed the review, which I always set up as a pre-test, then they should be ready for the unit exam.  If they weren't then they hadn't tried hard enough and too bad.   Now I feel bad for my students of that time period!   Once you make the shift to "learning for all" and "moving learning forward" for the students, then redos/reassessments make sense!   Why wouldn't we want our students to be able to demonstrate understanding of an outcome, even if it is two months after the formal lessons in class?  Ultimately the goal of the course is for students to have demonstrated learning in all outcomes.   Why we have set dates for this to happen is beyond me!  The curriculum states that the student will demonstrate an understanding of.... by the end of the course, not by October 15, when I have decided to give a "unit exam"!

Rick Wormeli has a great video where he shares his views as to why we should allow reassessments.  You can click here to watch part one of this video.  Click here to watch part two.

Here are some of the hurdles that I hear to giving reassessments and my solution to them:

"If I allow reassessments then kids won't try hard the first time"
Well in some cases this is true.  However, I have discovered that if you present this in a certain way then those will be minimized.  I tell my students that it is important to do the best you can on the first try because in the end, if you jump around with your levels of understanding then I will look for the most consistent level.  They know that if they consistently improve, then I will give them their final score, so the first ones won't count, but if they jump around ie.  2, 3, 2, I tell them I have to look at consistency and now that first assessment holds some weight.   Because of this, most students will do the best they can on the first attempt.  But yes, there are those that won't... we simply have to worry about what we can control!

"If I allow reassessments for everyone then the high achievers will keep rewriting until they get the 4 because they want the scholarships and they might write 10 times to do this."
In three years of experience I have yet to come across this.  I am not saying it won't happen and we might have those one or two students who do this.  I say let's cross that bridge when we get there.   I think that with the way things are now set up this won't be a problem.  But I might be wrong!

"How is it fair that a student who scores a 3 on their third attempt is the same as the a student who scores a 3 on the first try."
It is about the student's learning.  The ultimate goal is that students will learn.  We don't go and ask our doctors how many times they had to write the medical exams before they passed.   They are all doctors now and it doesn't matter.   Some babies learn to walk at 6 months and some not until 18 months.  Should we penalize the late walker and say they can never play sports?   A level 3 is a level 3, no matter when they achieved it.   Ultimately they now know the material.

"It will be time for me to create and score all of these extra assessments.  What does the student have to do?"
Well there is a cost associated with reassessing.  I don't allow my students to walk into my classroom and say "I want to rewrite outcome 5."  They have to show me that they have done some work in preparing for this outcome.  Whether it be making the corrections on their last assessment, or showing me that they have now completed all of their practice questions, or doing an extra set of practice questions, or simply having a conversation with me, they have to have put in some extra time before they get to reassess.  It's not a revolving door where they write, get back a low score and walk in to write again.  There has to be work done in between.  This work must be shown at least one day prior to wanting to reassess.  As far as creating these, yes, it is a little extra work, but ultimately I feel my job is about helping students learn and this is one part of my job.  With math, it is pretty easy to change numbers in a question.  Level 2 and 3 questions which tend to be process problems, are easy to change.  The level 4 do require a little more thought on my part, but when I am developing the learning plan I try to create  a bank of level 4 questions so that I can easily pull from this.   Depending on the outcome and the extent of the misunderstanding in the first assessment, sometimes I simply do an oral reassessment.  If I have a conversation with the student and they are able to explain their understanding then that is good enough for me.   It is really not a lot of work and in the end it benefits the student.  It also makes my job easier in following classes when I get these students as they now have a higher level of understanding than if I didn't allow for the reassessments and learning to occur.

"I'm going to have so many assessments to mark at the end of the semester when all of a sudden they realize they don't have the scores they want."
Yes, this was a problem.  However another colleague and myself have found a solution that has worked.  We have set up a reassessment policy that is communicated to the students and signed by the students and their parents.  We have set up contract dates at the start of the  year.  They are 3 - 4 weeks apart.  At each date, any student who is below a level 2 on any outcome is placed on contract.  They then have until the next contract date to attempt this outcome again.   The other colleague and I each take a noon hour a week to supervise these reassessments, so the student has two days a week to complete this.  This keeps the students more organized and spreads out the assessments over the course of the semester.  We also have a final reassessment date about 2 weeks prior to the final exam.  After this, there is no reassessing.  The final exam is the reassessment.  The students are all aware of these dates and it keeps things moving smoothly.

"In the real world you don't get a second chance."
Well that is actually false.  There are many instances where people have redos!  Going for a drivers license is one that most people will experience.  Not everyone passes on their first attempt, yet that isn't held against them when they go the next time.  We don't have stickers on our vehicles that say "I passed on my fifth time".   Airplane pilots did not land an airplane on their first attempt.  They practiced hundreds or thousands of times in a simulator before attempting with a real aircraft.    Accountants have more than one chance to write their exams.   Lawyers have more than one chance to pass the bar exam.  This list could go on and on.  School is about learning.  Failure is a part of learning.   Moving forward and becoming better is a part of learning.

Reassessments have worked well for me when a student walks in on an assessment day and says that they are not ready for the assessment.  I now tell them that it is okay, they can try the assessment, do the best they can and then we'll know what they still need to work on.  Usually the student is more prepared than they think.  Test anxiety is removed when they know there is another chance if needed.  Many times the student doesn't have to reassess, they simply weren't confident enough and are still programmed that all assessments "count" towards their final grade.  With that not being the case anymore, the student is more relaxed and often finds that they are more prepared than they thought!

Reassessments are not a bad thing.  I now not only allow reassessments, but encourage them.  I want my students to WANT to learn and WANT to show mastery.  I encourage them to be the best they can be.   I apologize to my students in the past when I didn't allow reassessments!

Friday, August 3, 2012

My Favorite Formative Activity

There are many different definitions and ideas of what formative assessment is.  Do you grade it?  Is it just feedback?  Is it an assessment?  A tool?  A process?  Dylan Wiliam says "Formative assessment involves getting the best possible evidence about what students have learned and then using this information to decide what to do next."  Embedded Formative Assessment, Dylan Wiliam, page 50.  I like this statement.  I want to find out what my students know and from there I need to make decisions on what to do next to move learning forward.

There is a lot of debate as to whether formative scores should be recorded.  I've adopted the idea that some of my formative "activities" are simply to collect evidence in an informal way, I will not score these.  The activity I am going to describe in this post falls in this category.  Other formative "activities" I will record and use these to assist with determining overall levels of understanding, "the summative score".  I think that Dr. Marzano best describes this when he says "a specific assessment is neither formative nor summative - it all depends on how the information is used.  Theoretically then, the same assessment could be used in a formative sense or in a summative sense."  Formative Assessment and Standards Based Grading, Robert J. Marzano, page 27.  He goes on to further say that "all assessments are in a sense 'formative'."  page 28.
In my class, I believe all of my formal assessments can be formative in nature.  The student has until the end of the semester to demonstrate deep understanding, so if a "unit test" at the start of the semester is improved upon by the "final exam"  then that unit test was formative in nature.

My favorite "informal" formative "activity" is one that has been routine in my class for about 5 years.  I got the idea from a colleague who did "3 minute reviews" at the start of her class.  It is similar to an entrance slip, but instead of testing what will be happening that day, I ask a question about a past skill/process.  It may or may not have anything to do with the daily lesson.  When the bell rings, there will be a question on the board and the students have 3 - 5 minutes to try and answer it.  For four and a half years, I had students put these in a duo-tang that were kept in my classroom.  I would look at them usually once a week.  They were not graded, just given feedback.  Each day, after the students had time to complete the question we would then take it up as a class.  Sometimes I would have a student put the answer up on the board, sometimes I would question a number of students on each step of the problem.   I loved this activity as I felt it was a great review.   I have had other teachers ask what they should do when at the end of a "unit" a number of students are still struggling with the concept.  In many cases I don't feel that spending one or two more days will be of great benefit.  However if you now do one question a day, for two or three weeks, the students will have the time to sort out their problems, and those who understand it won't be bored.  In my math 9 class, three of the first four outcomes that we learn are rational numbers, polynomials and solving linear equations.  I now have the entire year to continually review these skills, which are essential to success in math down the road.

In about April this past year, I watched the following video that was posted on twitter from The Teaching Channel.  It changed how I went about these entrance slips and has given me better feedback,   instant feedback, and it has given the students better feedback, so learning moves forward at even a quicker pace!  Click here to see the video.  The teacher was doing something very similar to me, except she went one step further.  She then turned the activity into an error analysis.  Brilliant!   It meant a slight change to what I was doing.  Instead of using the duo-tangs that I was, or the index cards she used, I took scrap paper and cut it into four pieces and I hand that out to the kids at the start of class.  They then hand them back to me as they complete the problem, I quickly sort them into yes or no piles, choose one from the "no" to rewrite on the board.  We then spend time going through this solution.  We find things that the student did correctly, we try to analyze where their misconception was, and we correct the solution.    It is instant feedback for the students and for myself and I find that learning occurs quickly.  One of my first attempts with this was when I was reviewing solving linear equations containing fractions.  It had been a while since we had done these in class.  I put a question on the board and discovered that only about 4 students had done it correctly.  The majority of the "no's" had converted the fractions to approximate decimals.  We went through the error analysis and discussed why this was not an exact answer.  The next day, I put a similar question on the board and I had about half of my class get the question correct.  This time only 2 students converted to decimals!  We were improving.  With this process I know how long I need to spend on the same type of question before we are ready to move to another skill.  I also know at the end of it which students now need some extra one on one help with the skill.  I love it!  This whole process takes 5 - 10 minutes, but it is well worth that time.  I don't believe I could accomplish the learning that takes place in this time in one period of extra practice on the skill.  I highly encourage trying this with your students!

Monday, July 23, 2012

Progress Reports

When I started on this journey three years ago, I wanted to simply add a visual bar graph to the student's progress report.  Dr. Marzano had shown studies that said this would improve student's learning.  At the time I didn't know why it would improve student's learning, but I thought it would be an easy addition. It lead me to where I am today!

What I soon discovered was that our division's gradebook was not compatible with outcomes (standards) based grading.  I needed a gradebook where I could group my outcomes, allow for individual student ordering of assessments, allow for professional growth in determining grades, allow for bar graphs, etc.  Our gradebook did not do this!  I looked at a sample progress report from Formative Assessment and Standards Based Grading, Dr. Robert Marzano, page 115 - 117 and wondered if I could create something similar.  My brother is a whiz with excel and he helped me get started.  Over the past couple of years our PLC has expanded our resources and asked people in our division who have a strong understanding of excel to create a gradebook that fits our needs.  It has really grown over the past year.  We have an idea, present it to these people and they tell us yes or no or they'll figure it out!  Here is what we have come up with:

This first picture is part of our first sheet in excel (it continues to the right for however many outcomes the particular class has).  It looks like a paper gradebook might look like.  The student's names are down the left hand column, but across the top it is organized by outcomes.  In this particular picture there are only 4 columns for assessments showing.  However I have hidden the columns that did not have anything in them.  So this sheet can be expanded to fit however many assessments you might give for a particular outcome.  Notice, there is also a current level for each outcome.  There is no magic formula for this current level.  The teacher inputs the value they feel best represents the students current level of understanding (I will blog more about this in a later post).  You might note that I have not changed the titles for the headings of each column - they are simply assessment 1, 2, 3, etc. other than the final.   This is because assessment 1 might be different for different students.  It is simply the first assessment for that outcome that the individual did.  As I am using the same scoring rubric for all assessments for that outcome, it doesn't matter if they completed a different assessment.  I no longer specify quizzes, exams, tasks, projects, etc.  They are all just assessments.  

This second picture is what gets created from that first sheet above (this pic has been saved as pdf, so the excel format isn't showing).  The first sheet (above) is where the teacher enters in their data.  Everything is then linked to another individual sheet that looks like the following.  This is an individual progress report.  It has the student's name (Student A) at the top.  It shows all of their assessment scores and their current level for each outcome and then it has a visual color coded bar graph (I will comment on the bar graph below).  We have also incorporated a comment box and a behaviours box.  You will notice that there is NO average or overall grade anywhere!  These are what the student gets at midterm when report cards are handed out, as well as many times throughout the semester as each teacher sees fit.  My students will receive hard copies at least once a month, but we often have mini interviews after each outcome or two when they will also see these.

I love this progress report!  I like that it shows exactly where the student is at on each outcome.  I like that it shows the progress.  I will communicate to students and parents that they should not just look at the current level, but look at the progress for each outcome.  Is their level of understanding improving?  Maybe they only have level 2 (yellow), but there has been growth from 0.5, to 1 to 1.5 to 2, so this student is improving.  I like this because it gives a clear picture of where the student is at on each outcome.  They can then refer to the specific rubric to see what they still need to learn to improve their learning.

In my class I will allow for individual assessments a few times through the year.  So when I have a short interview with each student to find out what they'd like to review and reassess, we look at this progress report.  It is amazing how many will simply say "I need to get rid of the red".  They do not like to see red on their report!  Yet, if it was just a number and no color, it wouldn't stand out as much!  I have also begun to ask parents at interviews how they feel about these progress reports.  I've asked them if there is too much information.  The comments are "these are great, with a quick glance I can look at the colors and see if there is a major problem occurring."   I now understand why the research shows a visual bar graph will improve learning.

The other thing that I like about this is that excel allows you to write comments for a particular cell and then you can hide them.  There is a little red arrow in the corner of the cell to show that you have a comment there.  I use this function a lot.  I can indicate if a student received help, whether the students were working in groups, used their notes, whether the assessment was formative or summative, etc.  I will also write reminders as to why a student received a particular level.  For example, if I gave them a 3.5 I will comment as to whether it was because some understanding was missing or if it was a calculation error.  Some students will get a 1.5 because they missed a term in level 2, but had lots of level 3 and 4 questions correct or some get a 1.5 because they were almost at a level 2 but no higher.   These types of comments are huge when determining the current level.  They are also helpful when having interviews with students and parents.  We can discuss what is holding them back from reaching the next level.

This past year we were watching some Rick Wormeli videos and one that fits with this can be watched here.  It was really neat to watch this video and realize that we are making many of these changes!

I am happy with where our progress report is at.  We are still tied to the gradebook that our division has purchased for submitting final marks.    Our division is also implementing a new gradebook at the elementary level (and soon the secondary level) that is suited for outcome based reporting, but as of yet, I haven't seen it produce the type of progress report that we are using or even one that will be similar AND provide the key information.  Through this experience I believe the key points that a progress report need to have are: 1) separation of outcomes 2)  progress shown and 3)  visual bar graph.   The format doesn't have to be exactly what we do, but those are key elements that have helped students move their learning forward and assist parents with understanding outcomes based reporting.

Sunday, July 15, 2012

Tracking Growth of Understanding

One of the student self reflection pieces I do in my classroom is have students track their growth of understanding.  I feel that it is part of my job to teach them a way to do this.  At the high school level we often assume a certain level of maturity, but we shouldn't.  Many students do not know how to self reflect and ask questions to guide their learning forward.  I ask my students if they know of a student who finished high school with really high grades, but then struggled at University.  Almost all students will put up their hand.  I tell them that it is important to be able to reflect on their learning and be able to identify any red flags that will hinder their success.  In University no one is going to teach them this skill, so it is important to learn it now!

Once again, I got this idea from Dr. Marzano, in his book Formative Assessment and Standards Based Grading.  He has a couple of examples of student progress charts.  One is found on page 82, another on page 87.  I first started by using the one on page 87.  I had a chart for every outcome for every student.   They kept these in a personal folder that were left in the classroom.   What I found with this particular chart, was that it was simply taking up too much space (I could only fit two outcomes on a page) and therefore was a lot of photocopying.  Another example of a continual progress report is found on page 103.  There is a free reproducible found here.  This is what I ended up using.  Our PLC group adapted it to fit our needs.  Here is a sample of one of my student's progress reports:
We left approximately 5 or 6 lines for each outcome.  We also added a column for reflection.  When a student received a graded assessment back, they were to chart their results.  Since I was assessing an outcome using the same rubric, a student could easily track if they were improving their understanding or not.  It is crucial, however, that the student charts their scores in the order that THEY completed the assessments.  

We talked about how they would want to be maintaining or improving each time.  We talked about if they dropped on an assessment, they should be asking themselves "why".  "What did I know the first time that I now don't understand?"   "What do I still need to learn?"

On occasion, an assessment would not test all four levels of understanding.  Maybe the maximum score on a particular assessment was 2.5.  I had students who received the maximum score star this in their charts.  That way, if they had a 4, 2.5* and then a 4, they would know that they didn't actually "drop", it was simply the maximum they could score.  

 I had students tell me that this chart helped guide them when preparing for a comprehensive assessment.  They knew which outcomes they needed more work on and which they had a pretty consistent understanding of.   This also helped them when an opportunity would arise in class to have a redo (I would have a few days a semester where it was "student's choice" assessment day).  With a quick glance of these charts they could see which outcomes still needed to be worked on. 

These continual progress reports are also great for students who typically struggle and take longer to become proficient with an outcome.  They will (hopefully!) be able to see growth happening.  Even if they are moving from a 0.5, to a 1, to a 2, it shows growth and we will celebrate this growth.  I had a student my first year of doing this who hated math, thought she sucked at it, and wouldn't try.  Once I got her to realize that she was actually learning, her whole attitude changed.  Yes, she was only at a level 2 after the outcome was completed (completed as in formal lessons done, my outcomes are never completed until the end of the semester!), but she had started at level 0.5.  We celebrated her growth.  She walked away with a smile on her face and a positive attitude followed her to class from then on.  

I will continue to use these growth charts, in all of my classes from grades 9 - 12.   Even if one student benefits from them it is worth it!

Wednesday, July 11, 2012

Outcome (Standards) Based Reporting

"In a standards based system, a student does not move to the next level until he or she can demonstrate competence at the current level.  In a standards-referenced system a student's status is reported (or referenced) relative to the performance standard for each area of knowledge and skill on the report card; however, even if the student does not meet the performance standard for each topic, he or she moves to the next level."  Formative Assessment and Standards Based Grading, by Robert J Marzano, page 18.

Two years ago, our math department was outcome-referenced (I will use outcome instead of standards as our provincial curriculum is by outcome).  We were reporting on the student's progress for each outcome.  However, we still looked at simply a "passing" average of these outcomes when determining if a student was to receive the credit.  We encouraged students to meet at least the level 2 of understanding on all outcomes, but it wasn't necessary to move on.

After reading the difference between standards based and standards references, we started to question whether we could make the move to outcomes based.  We wanted to, but were a little afraid of that step.  We had already made so many changes to our philosophies and to our policies, we weren't sure we could handle another large "shift".  We still had colleagues in our PLC that were still trying to understand and make the shift to outcome referenced reporting.  We tossed around ideas of students having to be level 2 on a certain percentage of outcomes, or certain "essential" outcomes.  After some debate, we finally decided as a group, with support from admin, that we would move to outcomes based.  We made this change this past year.  We communicated it to all students and their parents.  We informed them that in order to receive the credit at the end of the semester, the student would need to have at least a level 2 on EVERY outcome.

I'd have students ask me "do you mean I'm going to fail if I just have one outcome below a 2?"  My reply would be "no you will not 'fail', but you will have to continue working on that outcome before the credit will be assigned."  We were not asking the student to repeat the entire class.  I would explain that this made more sense than the "old" way as now they would be better prepared for the next level as they would have met a basic understanding of ALL outcomes.  I asked them to reflect on where they were currently at with their feelings towards math.  If they struggled with math, I asked them to reflect on whether they felt they had "passed" all parts of math in the past.  We then talked about if you don't "pass" everything, then the next year it is harder to learn the new outcomes, which in turn means you may "fail" more outcomes again, which will lead to more frustration at the next level.  When explained this way they nodded and agreed that outcomes based made sense (even if they didn't like it!).   Outcome based also means a student can't ignore an outcome that they are finding difficult and still pass the class.  They HAVE to do the work!

We are very fortunate at our school (it is a large school - approx. 2000 students), to have an extensions campus.  Students are able to take courses on their own, by completing work through modules, or online, etc.  So it was pretty easy for us to say that if a student had not met the requirements by the end of the semester, they would simply enroll with the extensions campus to complete the required outcomes.

We also realized that many students would struggle with continuing to work on an outcome they were  struggling with on their own, so we set up some structures to assist them.  Our school hired a grade 12 student who was strong in math, to provide free tutoring 3 hours a week after school (1 hour a day, 3 times a week).  For our grade 9 students, the math 9 teachers rotate through 2 days a week of noon hour extra help.  For grades 10 - 12, teachers provided their own noon hour extra help.

Another teacher and I joined forces to allow our students two noon hours a week for help and to reassess.  We each supervised one of these days a week.  We also set up guidelines to help students organize their time.  We didn't want them to all of a sudden, at the end of the semester, realize that they needed to reassess a ton of outcomes.  We came up with a policy and had student support dates.  On these dates, any student who had an outcome below a level 2 would be put on a "contract" and given 3 - 4 weeks to ask for help and reassess.

The first semester we implemented this we knew we may end up with some unhappy or surprised parents/students.  We communicated it over and over, and sent out letters to parents reminding them of the policy.  One of the things we stressed in our PLC group was that we had to stick to our guns and the final progress report could not have any current levels below a 2 if we were assigning credit to the student.  The minute you break what you have stated, it no longer holds weight.  At the end of the semester we had a number of students who had not met the criteria.  We made the appropriate phone calls to parents informing them that their son/daughter was not receiving the credit at this time and recommended one of two options to them.  If we felt that the student actually did need to repeat the entire class with a teacher, then we told the parent this.  We had very few students fall in this category.  With all of the support provided along the way, there were not many students left in this position.  The other option presented was that their son/daughter would register with the extension campus to complete the outcomes, and once successful the credit would be applied.  We were pleasantly surprised as to how many parents and students were thankful for this opportunity.  "You mean I don't have to repeat the entire class?  Thanks!"   There were very few unpleasant conversations.

The second semester with this system went a lot more smoothly.  We found a couple of things second time through.  One, the students now believed that we were going to follow through and they knew they had to work to achieve a certain level of understanding and then maintain or improve this level.  Two, we found that teaching the next level was far easier than it had been in the past!  Instead of having to re-teach a skill that was necessary for a new outcome, I only had to review it!  Since all students sitting in my class had met the basic level of understanding in the previous class, I wasn't speaking Greek to some of them!  We were able to go deeper with outcomes as the time was there to advance instead of back up.

It was interesting as we met after semester 1 to reflect on how things went, that the issue of "grades" came up.  We still have to convert to a percentage at the end of the semester (grades 10 - 12 only) for the Ministry of Education.  We only converted if the student was receiving the credit, which meant they met the requirement for all outcomes.  If they hadn't then there was a "blank" on their report card where the grade would have been.  The comment a teacher made was that their marks seemed quite high and their class average was a lot higher than before.  I had to grin.  Yippee!!!!  That means you had students who LEARNED and are proficient with what they are supposed to be!   Dylan Wiliam says "we should set a goal of proficiency for all, excellence for many, with all student groups fairly represented in the excellent" Embedded Formative Assessment, page 22.  We need to stop norm referencing and thinking we can't have a lot of students at the top of the class!   Also, because we were now only assigning "grades" to students who had achieved EVERY outcome, there were no "failure" marks being factored into the student's grade.

We have learned from this year that it is very important to communicate regularly with parents on how their son/daughter's progress is going so there are no surprises.  It is also important to realize we are still dealing with kids, and they need help organizing their time.  We work on having students track their growth and take ownership for their learning, but we guide them with structure and provide reminders (contracts) to help them achieve.

Monday, July 9, 2012

4 Point Rubric

When I started this journey three years ago, I sat and listened to what Dr. Marzano was saying about the need for a new scale for assessing and grading.  I heard him talk about the 100 point scale being inaccurate.  He says "it is like measuring the physical growth of a student throughout the year but using a measuring tape that changes how long an inch is from one measurement to the next."  Formative Assessment and Standards Based Grading by Robert J Marzano, page 41.  He did an activity with the people in attendance to prove his point.  I was amazed at how a group of educators could be so far apart when scoring on the 100 point scale!   He then furthered this activity, showing how we would all agree on the same score if we used a 4 point scale.  (Formative Assessment and Standards Based Grading, Chapter 3)  I was sold!   

With some help from a couple of colleagues, I spent the next 6 months developing rubrics, trying them, revising them, before being challenged by my admin to come up with a general math rubric.  When I look back now, I realize how poor those first few rubrics were!  We were trying to take what we had from an assessment and fit the results into a 4 point scale!  It wasn't working!   So we sat down and read more from Dr. Marzano (he speaks of this scale consistently in many of his books!) and adapted his 4 point scale to fit our needs.   This is what we came up with:

Level 1:  This is pretty much bang on to what Dr. Marzano recommends.  We don't define skills/processes/knowledge/etc. at this level.  The student is simply inconsistent or needs help with the outcome.  

Level 2:  Dr. Marzano defines this as "simpler content" (Formative Assessment and Standards Based Grading, page 48).  We defined it as the "basic level of understanding" for the outcome.  We expect all students to be able to achieve this level to receive their course credit.  These really are the basic skills, and if a student is unable to be successful with these types of questions, they are not ready to move on.

Level 3:  Dr. Marzano defines this as "target learning goal"  (Formative Assessment and Standards Based Grading, page 48).  We have also set this level as the target level of understanding for the outcome.  We look at what the OUTCOME says needs to occur (not necessarily the indicators), and make sure that they can achieve this for level 3.  

Level 4:  Dr. Marzano defines this as "more complex content" (Formative Assessment and Standards Based Grading, page 48).  I would have to say we again, are pretty similar.  Here is where we look for deep understanding.  Many application questions are at this level.  Error Analysis is often found here.  We look for explanations of work, theoretical understandings as opposed to simply memorizing a process.  

Once we had agreed upon what each level would mean, we then had to sit down with each outcome, decide if we would leave the outcome as one piece, or "chunk" it ("unpack it") into smaller, more communicable pieces.   We then had to create outcome specific rubrics that following our general rubric.  This is what takes the most time!   We have discovered through experience that sometimes you will try one rubric only to discover that it needs to be tweaked/combined/broken up and that that is okay!   We will likely never have the "perfect" rubric!  What we do have are rubrics that are allowing us as teachers to be more consistent with each other and between students.  We are also now very transparent for students and parents with what is expected!

We have also discovered that we often have two types of outcomes.  The first is an outcome that has definite progression in the learning.  These outcomes are easier to make the rubric.  For example, solving linear equations - our math 9 rubric has level 2 is solving when there are up to three steps and no fractions; level 3 is solving any linear equation; and level 4 is situational/error analysis/explanations/modeling, etc.  

The second type of outcome is harder to define.  This outcome is one where there are many distinct pieces and not always in sequential learning.  We have also been encouraged to stay away from quantifying levels (ie.  "able to do three of five of the following...").  So this has made these type of outcomes the most difficult to write a rubric for.  Here is an example of an outcome from the Saskatchewan Math 20 Foundations course that is of this type.  The description in the colored boxes are our general math rubric I described earlier.

What we decided for this outcome was that the level 2 skills were basic definitions.  There was no manipulation of formulas/equations/etc.  We felt that because of the formative procedures in place a student would have lots of feedback and by the time the end came along, they should be able to answer all of those terms successfully.  The level 3 skills require some sort of manipulation or solving.  There is more to these skills.   Level 4 is still a deeper understanding.  You'll also notice that we wrote these in student friendly terminology.  When a student reads the rubric they read "I can determine..."

Every "graded" assessment, no matter what type of assessment (quiz/exam/performance task/oral/etc.) will be graded using the specific outcome rubric.  This allows for tracking growth of learning.  It is a consistent scale.  It does not change from assessment to assessment.

We have now created these specific rubrics for all of the Saskatchewan Math 9 - 30 curriculums!  We are constantly tweaking them, but there is a starting point!   We have also decided as a department and extended division PLC group that we will share these rubrics if others want them.  A person might not agree with every one of the rubrics, but they are a starting point to be used.

On a side note, we do assign levels of understanding using half points as well... 0.5, 1.5, 2.5, 3.5... but we do NOT define these with skills/processes/etc.  We use what we learned from Dr. Marzano in that these are used for students who are completely successful with a lower level and partially successful with a higher level.  I believe the half points are very important for a student so that they can see growth in their learning.

It has been two full years of using the 4 point rubric instead of the percentage.  Our students do not see a percentage on ANYTHING, even report cards, until the final report (grades 10 - 12 only) and ONLY because the Ministry of Education requires it.  It did take some time for students and parents to adjust to this change, but my last set of parent teacher interviews in April were the first time I did not have one parent ask about a percentage!  I feel we are making progress.  We have been communicating a lot better with parents, through letters, videos and emails as to why we are changing.  Once you explain to them that this is a much more accurate representation of what their son/daughter does or does not know they buy in.   I will tell them that in the past, if they saw a 75% did they really know what it meant?  Did it include behaviours?  Did it mean that the student scored 75% on every outcome?  Or did it mean that the student had 50% on three outcomes and 100% on three outcomes?   Did it mean the student had been successful with all outcomes?  Did the student improve their learning through the course?  A 75% does not tell you much of anything other than it norm references kids and people have their own opinion as to whether 75% is good or bad.  It is often referred to as "average".  However, if you see that your son/daughter has level 3 on outcome FM20.9, you can read the rubric to see what they have been successful with and what they still need to work on.  Our progress reports (which I will blog about soon), will also show what the student's levels of understanding were over time so that the parent and student can see if learning is occurring.  The mark is pretty transparent.  Nothing is hidden.  Since making this change I am very confident in defending a student's "grade".   When a parent comes in and asks what their son/daughter still needs to work on, I can give them an accurate answer!

Parents are also concerned about University entrance.  How will this affect their son/daughter getting into University?  I tell them two things.  First, we will still give a percentage at the end of the course so that they can apply (we have a conversion that is common to our department).  Second, I tell them that this is far superior to the past system, as now if a student knows that they want to go into a program that has very competitive entrance requirements, the student knows what they need to learn to have a deep understanding of each outcome and can work towards those higher "grades".  In the past it was often a one shot deal.  You learned the outcome, wrote the test, and moved on.  Now we track growth, encourage growth, provide opportunities to improve, and basically give a checklist of what needs to be done at each level of understanding.   Parents accept this when it is explained this way.

This has been a huge philosophical shift for everyone involved and although we are not all at the same place in this shift, we are moving towards a common goal!  That is we want all kids to learn!  We need to find the best way for this to happen and to me, the 4 point rubric is a definite piece of this journey.