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!!!!!

7 comments:

  1. I am right there with you! I teach 8th grade algebra in a community where most parents took algebra in late high school, if at all. I totally understand that with a lot of these skills, they fall into "if you don't use it you lose it." When parents tell me they don't remember it or didn't learn it this way, I always say I understand and I back them up. I also let them know that I am not a teacher who forces my way upon students and if their student can understand it the way their parent teaches it that's fine.

    With that, I CAN'T STAND this "new math" argument. Where did that term even come from? My (students') parents just accept their children struggling because they did or tell them it's not important. During a conference I had a very much struggling sixth grade student tell her mother that "math is important. Like if you go to the grocery store and your total is $17.43 and you give them a $20 you need to make sure you get back..." and started trying to figure out the change. Her mother said "You get back $2.57 - that's not math it's common sense." That just broke my heart to see a student who constantly fights me to be just torn down by her mother.

    The hardest thing about being a math teacher: fighting back against the attitudes learned from parents.

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  2. Hi,

    I came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we're putting together. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter -- bringing math to children in an innovative, adventurous way. I’d really appreciate your help in getting the word out about the project.

    http://www.kickstarter.com/projects/564889170/the-number-hunter-promo

    I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We're teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

    I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.
    Our concept is to create an exciting, web-based TV show that’s both fun and educational.

    If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you'd be interested in link exchanging (either on The Number Hunter site, which is in development, or on StatisticsHowTo.com which is a well-established site with 300,000 page views a month) please shoot me an email. We're also always looking for input and ideas from other math educators!

    Thanks in advance for your help,

    Stephanie
    andalepublishing@gmail.com
    http://www.thenumberhunter.com
    http://www.statisticshowto.com
    http://www.kickstarter.com/projects/564889170/the-number-hunter-promo

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  3. Thanks for this eye-opening post! And I do agree on your point about embracing the new strategies. The rules of math are constant, but over the years, new techniques are developed on how to solve and calculate things. It is your choice, if you want to go the traditional way or learn the new one. But it wouldn't hurt to learn both, as you can gain a new perspective on solving things.

    Yvonne@HomeTutorsSacramento.com

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  4. Loved this post I will be referring people to it when I hear this argument, which I seem to again and again. You do a wonderful job of explaining this "new math".

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  5. I ran across your post, when looking for another similar argument, that also made reference to the medical procedures. As the parent of a third graders, most of us are 30 or younger, and still feel like we should know the most up to date information. I understand it enough to help my son, and I work on it daily, as the mother of an Advanced Student, who just brought home all A's on his progress report, except one... His math grade is a low B. I feel I need to understand it to be able to help him, and the more I understand it, the more I stand behind it. Thank you for this wonderful article, to help me help others see, even when looking from the eyes of the parent of a young child!

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  6. I'm sorry but I do not agree at all when it comes to the new curriculum used in elementary education. The new curriculum is anything but helpful at teaching kids an efficient way of solving mathematical equations on the core level. When we grew up, we were taught multiple methods at solving problems as well and were told to use what works best for us to get the correct answer as long as we showed our work. I understand for the most part that this is still the case, but the primary teaching methods of this new curriculum has led only to the confusion of the students. When they spend all day learning these "new" methods and look more confused then when they started, that's a problem. Especially when reverting to the "old" ways they seem to understand it in minutes. I also feel it is fairly ignorant to compare the strategies of teaching math to the use of medical procedures. Maybe it's just our area, but there is no multiple methods taught anymore. The schools are forcing these new strategies as the only way at deriving the answers and that is where most of our frustration stems from. Our friends child, although all answers were correct, received a 0 on his work because he didn't do it there way. When taken to the principle all they got was a "sorry our hands are tied, that is how we have to do it". Maybe if we had more teachers willing to acknowledge the fact that there is more than one way we wouldn't be facing these problems, but that is not the case here. I am in no way condemning your point of view but to downplay the concerns of parents and teachers on this topic is wrong. Everyone has the right to their own opinion and should feel open to expressing them. It is topics like these that support the ever growing number of home schooled children and the statistics of there achievements surpassing our public educational system.

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  7. I have to agree with Keith on this one, the problem I have is our school has a math teacher that's more concerned with his athletics director position than a math teacher. I can help my children and they understand, but if they use my (old school) equation and turn in the work it's counted wrong. explain this one. The teacher and I have the same answer but my way is wrong but understandable to my children.

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