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!