Monday, March 31, 2014

Flex Groupings


Last semester at one of our division math PLC meetings, our math coach talked about Daily 5/Flex Groupings that some elementary teachers were trying in math.  The idea was adapted from the Daily 3 or Daily 5 that is done with reading at the elementary level.   I was intrigued by the idea, so researched it a little more and thought about how I might incorporate it into my math 9 class.  I decided that I would try it in semester 2.  I looked at the outcomes I had left to work through and decided I could afford to use Mondays as a flex grouping day.  I figured we could use that time to review outcomes that needed work, based off of the data I was collecting.

So this semester I have started to use flex groupings in my math 9 class.   The students are split into groups, and these groups are flexible, so each week they will be with different people.  It depends on the outcome we are going to be reviewing.  I use the data I have collected from assessments to group the students for that week.   The different groups I may use are:  math with a teacher, math with a partner, math on your own, math in a group and math with technology.   Depending on the topic to review and the time necessary, I may have 3 – 4 rotations in a day.   I will always use math with a teacher as one of my groups.   This is the most beneficial one.  I will usually group students based off this group.  Whichever outcome we are working on, I look at my data and take the three or four “weakest” students based on their data, and put them together, then the next three or four in another group, etc.  For the 12 – 15 minute rotation that they are with me we will work through one question at a time and I can see what they are misunderstanding and we can talk about this and find a way to help them understand better.   It has been amazing how impactful this has been.  I have discovered with a couple students, that what I deemed as “rushing through the work” and being careless, was actually a misunderstanding about double negative signs.   With other students, just having me sit there as they worked through a couple of questions, discussing with them what they are doing right and where they are making mistakes has helped them to understand.  

When they do math with a partner, I have deliberately grouped them so that one partner is able to help the other partner.   For the math by myself and math with technology, it is more about reviewing and becoming more consistent with basic math facts.   The math with a group is about problem solving and logical reasoning. 

In order to do this, you need to teach the students how each group is supposed to work.  If I need that 12-15 minutes with my students who are with a teacher, I can’t be monitoring the rest of the class.  As a result, we “practiced” each group before we formally started this process.   The guidelines we set up as a class are:
*          Gather & set up materials quickly and quietly
*          Get started right away
*          Work quietly
*          Stay in one spot
*          Be respectful of classmates
*          Work with math the whole time
*          Build your math stamina
*          Grow in your understanding of math
*          Put materials away quickly & quietly

The students have been following these guidelines pretty well.  They seem to enjoy this strategy and when I missed a Monday (the day I have chosen to use this),  they asked me on the Tuesday if we could do “Monday math”.  So as a teacher I am seeing improvement with the students understanding, and they are enjoying the process as well.
 

Thursday, September 5, 2013

Communication with Parents

This year a school goal of ours is to send out "group" emails to the parents of the students in our classes.  We can pass on information that way.  Our PLC has decided that we will send out a minimum of 4 group emails each semester.  I hope to send more.  It is so easy once you have your contact list made up.   I'm sure there are some parents who don't want to hear what is going on, but I bet there are more that do enjoy hearing these things.  I wish I received emails from my kid's teachers.  I actually sent one to them this year telling them a little about each of my kids.

This year I sent one of my emails out prior to the first day of school.  The email simply introduced myself and the class I had the student in.  It reminded them of the schedule on the first day and the remainder of the year.  In the last paragraph I gave a brief overview of the course.  One of the other paragraphs I borrowed from another colleague:

"I would like to invite you to send me an email introducing yourself and/or your student to me.  I would love to hear about things that interest them, their strengths and weaknesses etc.  Be sure to include their name in your email."

Some of the responses I received were really neat.  I learned some interesting things about both the parents and the students.  I was surprised at the detail some put into their responses.   Although I did not receive a lot, the ones I did receive I enjoyed reading and was sure to thank the parents for their email.   This is something I will continue to do each semester.  I'm hoping more parents will start to respond.


Wednesday, August 21, 2013

My opinion on standardized testing

Last semester I had an opportunity to be seconded by our Ministry of Education to help write questions for the math departmental exams.  My students do not write these as I am an accredited teacher.  However I thought this would be a great opportunity to learn from others and see where our Ministry is headed with standardized testing.  In the last year our government (Saskatchewan, Canada) has pushed out an initiative to give standardized tests to students starting in grade 3.  I have to say I was not a fan of standardized exams prior to my experience, and after it I am even less of a fan.  It is not that I am afraid of the test as some will say teachers who are opposed are.  I do have a number of reasons for my opposition and would like to share.  These are just my opinion.

My first reason is fairness.  I am struggling with the lack of uniformity for terminology and notation.  The curriculum is not specific enough in many of these cases.  Resources use different notations and terminology.  The pathways have used different terminology and notation!   The curriculum states that students do not have to know all strategies, but they have to be able to do one of them consistently.  I may show all strategies, terminology, notation in my class, but allow students to focus on what makes the most sense to them.  Now they write a standardized test where the developer has picked a notation that they may not have focused on.  Yes, they may have seen it, but it doesn’t mean they understand it, yet they may very well understand the concept, but be unable to answer the question because of the terminology.  I think of domain and range and interval notation vs set notation.  My studdents are split among those two notations.  Yet do they understand domain and range?  You bet.  But on an test like this some may get it wrong, not because they don’t know domain and range but because the notation is not familiar to them.  This is a huge concern for me.  If I had to give a standardized test I would lose the flexibility in my classroom to allow the learners to learn what is best for them.  I would still show all forms, but would say that “this will be what you will see on the standardized test so be sure to know it”.  That so defeats the purpose of our new curriculum and our learnings about learners. 

My second reason is the format.  I do not believe you get a good indication of what the student has learned through a multiple choice format.  There is too much guessing that can occur, or working backwards, or redoing until an answer matches (trial and error).  No one is looking at the work to see what has actually been understood.  How will the results be distributed?  Indication is they will go to the parents and teachers.  Will there be one score?  Question by question results?  Outcome results?  What outcomes will be assessed?   The indication is that they have to be able to be computer scored so the results can be returned asap so that these are deemed as "formative".   What outcomes then will be tested?   How will this be communicated to parents?  Will parents be told that this is simply a snapshot and that the score may be inflated or deflated?   If the test is given towards the end of the year then they are not formative in nature. 

My third reason has to do with the move towards standards (outcome)  based assessing/grading/instruction.  In a standards based classroom, every assessment is done according to the outcome.  It is assessed by level of understanding, with the same rubric each time.  It is not about accumulating points, but in growing the understanding.  In our classrooms, we do not assign a weighting to the final exam.  The students know that if they show growth of understanding they receive that level as their final.  If they do not maintain their previous level of understanding, their overall level will drop and they may even have to come back in for more learning.  We do not allow a student to skip/ignore/leave blank any questions at a low level of understanding or they will have to come back for a conversation.  As a result, the majority of our students actually improve their levels after the final.  This all changed when we took away the percentage weighting on the final.  At that point many students were simply calculating that they had enough “points” to pass or get the mark they wanted.  Now they have to demonstrate understanding on everything.  I think the standardized test will really hinder classes trying to do standards based grading.  They are not set up by outcome, using a common rubric, and assessed by outcome.  There is one score assigned.   This is not an effective assessment method.
 
I get that we are living in a world where accountability has become a huge issue.  However I do not believe that these will make teachers "accountable".  I do not believe the data will be an accurate indication of what is going on in the classroom.  I think that if the government wants to improve teachers and learning, they need to think outside the box.  Dylan Wiliam’s philosophy is that we can’t get rid of the poor teachers, but we need to work with them, support them and help them become better teachers.  I do not believe standardized testing is going to do this.   This is just my opinion.
 

Friday, June 7, 2013

Communication Tools

One of our goals as a department this year were to create some videos for parents and students to help with understanding our progress report and rubrics. Two of these videos have been created.

The first one is about “How to Read the Progress Report”. We know these can look different from elementary reports and from other subjects, so we want to help parents and students to understand them. They are a communication tool and need to be used that way! I hope this video will help with this.

The second video is about reading the rubric. Again, the rubric is a communication tool. It is not only for assessment purposes for grading. In fact, the student should be using it to prepare for assessments. It can be used as a checklist to be sure that they are prepared for the assessment. Here is the video on reading and using the rubrics

I hope these videos will assist the communication process and the understanding of the outcomes based system.  

Tuesday, June 4, 2013

A Step Backwards

I've been blogging about our school's journey the last four years towards being standards (outcome) based.   Recently I feel frustrated as I believe we are being pushed backwards into standards referenced.   Currently, and for the past two years, we have been truly standards based where a student has to meet the basic requirements on ALL outcomes in order to receive credit for the class.  It was at a supper meeting with Ken O'Connor where we decided to do this.  He asked us why we were allowing students to not meet a requirement in all outcomes.  When he said it, it seemed like a no brainer.   Robert Marzano promotes standards based.  Other researchers have done work with standards based.  We have worked hard as a department to promote and implement this.  Students have risen to the expectations we have set forth.  I know in my gut there are successes from this, and the data is beginning to show it as well.  More students are being successful.   A comment today in our math PLC was that students in the 30 level classes are doing very well.  It was almost a surprise to some.  Then when we thought about it we realized that it is likely because we have expected these students to learn ALL outcomes to a basic level in previous classes.  You now have students who just need a review of the pre-requisite skills, instead of needing to be taught them because they never learned them before.   Sure there have been a few hiccups along the way, but that is to be expected.  All in all, this system has been better for the students.  They are earning their credit, and even if they don't retain all of the math skills, they are learning work ethic and the satisfaction that they earned what they got.  They are no longer able to ignore something because it is a little difficult for them.  Education is about doing what is best for all learners and from what I have seen the past two years, this is a better system for the students.

Recently we have been informed that our expectations may not follow Ministry regulations and that we might not be able to expect a minimum level on all outcomes, thus not allowing us to be standards based.   We have researched and looked through Ministry documents and really can't find anything that doesn't support what we are doing.  We found a document, Renewed Curricula that the Ministry put out, and on page 12 found this statement:


Outcomes define what a student is expected to know and be able to do at the end of the grade or Secondary 
Level course . Therefore, all curriculum outcomes are required . Indicators clarify the breadth and depth of each 
outcome.

To me, this is stating that all outcomes are required.  Today, at our meeting we discussed communication from the Ministry that stated a 50% is required to receive credit, but nowhere did it say how the 50% was to be determined.  It did NOT specify that it needed to be an average, or the mode, or the median.  It was just 50%.  Thus I don't think what we are doing contradicts anything in Ministry documents.  I would love for someone to show or explain to me how we are.  Until someone can do this, it saddens me that we might have to move away from standards based.  We have seen success in the past two years with it, and there are multiple research studies showing the benefits of this system.   It's a little frustrating to think that we might be taking a step backwards.  I'm open for change, but I want the change to be forward thinking, not backwards.  I am hoping that this is just a conversation that is happening and it will not become a reality.      

Friday, May 3, 2013

Questioning Techniques

Today I attended SUM 2013.  I was very excited to hear Dan Meyer speak.  I've mentioned him in previous blog posts.  We have tried to model his teachings, but it is not an easy task!  It was great to hear him today and have him take us through a three act math activity, modelling to us what a teacher's role is.   He has a very good way of questioning so that everyone feels like they CAN ask a question and that every question is valid.    He shows a problem/situation/activity and then asks for "the FIRST question that you have".   He typed out any question a person asked and never made you feel like it wasn't good enough.  

Fast forward to the last keynote speaker.  This person would ask for questions, but if they weren't what she wanted she responded in a way that I can only describe as somewhat rude.  There were two questions in particular that I didn't like how she responded.  One wasn't along the lines of what she asked, but instead of thanking the person for taking a risk, she more or less shrugged it off and asked for a question "with words".   Another time she was asking what questions could be developed from a picture she was showing, and with one of the responses, she turned her back to the person and commented "I don't think students would find that interesting."    Really?   If I did that in my classroom with my students I would NEVER have a student risk taking!   After the second "snub" I basically tuned her out.  I didn't find her respectful of her audience. 

The two differences between the keynote speakers really opened my eyes to how a teacher can turn on or off students in a heartbeat!   We have to be very careful how we respond to student's questions and comments.  We need to encourage thinking, and thank students when they do take a risk, even if they aren't necessarily on the right path.  I definitely want to model Dan Meyer's technique, and avoid at all times, the second keynote speaker's technique!  

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!!!!!