new math

[pseudoreality]

I noticed in the STEM thread you mentioned you are trained as a math teacher. Would you be able to provide a summary on the new math I hear so much about? There has been some high profile complaints about it and how our students are underperforming in math skills because of it.

Last weekend I attended strategic development workshop for the NWT & Nunavut Association of Engineers and Geoscientists (NAPEG). At the retreat we discussed community outreach and our education foundation which distributes a couple of scholarships. The current President of NAPEG works part time and does volunteering/substitute teaching at the schools. He mentioned he was shocked on how the kids just can't do math. In his opinion students are taught very abstract theories and not basic skills. This really concerns me for the future of our country. I know the federal government is doing everything they can to import technically trained people, but it probably would not hurt to train one to of our own to do those jobs.

My belief is kids first need to learn the fundamental skills. Once those skills are second nature, then the kids might be able to appreciate some of the abstract beauty of math.

Lastly, I would like to thank you for being a math teacher. I believe one of the challenges for schools in teaching STEM is finding good educators skilled in those areas. People who are skilled in the math and sciences can often have other much more lucrative career opportunities. Therefore, whenever I see a good math teacher I know they are in it for the right reasons.

[DataDoxy]

I appreciate your query. This is currently a big issue in Alberta as math performance of students is slipping in the ranks according to international standardized test scores (PISA, 2012). As such, many people are questioning whether we should go “Back to the Basics” or continue to embrace the “New Math”. This is a pervasive problem and it can be confusing as both sides of these Math Wars continue to point fingers at each other.

I have been a math teacher for ten years and a mathematics education researcher for the past seven years. During this time, I have seen first-hand how many students are falling behind in math and it concerns me greatly. This is precisely why I completed my doctorate in this area as I am determined to change the equation so to speak. During my years of research, I have come to the conclusion that the problem is not just what math is best, it is also about how we, in Canada, train our teachers. I will address both points.

The Basics vs. The New Math

There is no question that students should learn their math facts as these are the foundational building blocks of math. When student do not know their facts they have difficulty advancing in mathematics as they struggle with the attainment of the higher level concepts which are built upon these foundational concepts. Additionally, many students that do not “know” their facts struggle significantly when solving complex or multi-step problems. This is because they are experiencing what we call cognitive overload as their working memory becomes over-taxed. In other words, these students end up using much of their mental energy finding the unknown math “fact” which they need to solve the larger problem which leaves insufficient mental energy to attend to the larger problem itself. Sadly, many of these students develop gaps in their learning and thus continue to struggle with math over the course of their lifetime. For example, I routinely hear many adults, parents and even teachers say, “I am just not a math person”. This belief is nothing more than a myth!

According to the latest neuroscience on learning, we now know that there is no such thing as “a math person” (Boaler, 2008; 2012). In fact, research states that everyone can become proficient at math (National Council of Teachers of Mathematics, 2000).

So… why the disconnect between neuroscience and students’ performance in math? The answer is simply that we are not teaching math optimally for the vast majority of learners. This is true whether we are embracing the Back to the Basics mentality or the New Math principles, but for different reasons.

Traditional Math & Back-to-the-Basics

Traditionally, the majority of classrooms have focused on learning the basics first through rote memorization first and attach meaning afterwards. Research tells us this process is backwards. Consider when we are learning to read, we understand what a cat is before we can read the word c-a-t. When we do acquire the ability to decode, we learn that c-a-t is in fact a “cat” which we have a mental picture of in our head and therefore, can attach the word “cat” to. We need to do this for learning math too! For example, it is more effective to understand what a group of two added to a group of three is conceptually before we learn the symbolic representation 2 + 3. Then, once we understand the concept of addition (and the concept of base ten) we can then apply this to higher level questions like 22 + 3 or 127 + 3.

Further complicating learning of math in schools is the weight placed on the speed and accuracy of math facts. Unfortunately, many traditional teachers tend to focus speed and accuracy long before students have made the necessary cognitive connections that we know need to come first. This can result in misconceptions that kids can carry with them for their entire math careers which can lead to further complications and misunderstandings.

In addition, when kids focus on the rote memorization of facts, they lack “number sense”. This is highly problematic as number sense is the foundation for all higher-level mathematics (Feikes & Schwingendorf, 2008). For example, research tell us that students who fail algebra (which is the gatekeeper to higher level math like calculus) often lack number sense (Boaler, 2012). Additional research stated that when looking at the difference between "high achievers" and “low achievers”, students categorized as low achievers were considered so because they lacked number sense (Gray & Tall, 1994). How is number sense attained? Number sense is developed when kids learn math conceptually first which is the principle idea behind the New Math movement.

The New Math

The optimistic ideals of the New Math movement lie in stark contrast to the traditional Back-to the-Basics movement. Personally, I see the concept of New Math as valiant and necessary, but misunderstood and poorly operationalized. I firmly believe in the goals of New Math as I think that kids need to understand math deeply so they can rationalize, problem solve, and be proficient in math at higher levels. These are the skills students will need to meet the emergent demands of our rapidly-changing, technologically-driven, 21st century world. Thus, the main problem with New Math in my opinion is not the idea behind it; instead the problem lies with how it has been implemented in our classrooms. This is because teaching the New Math as it is intended is complex and time consuming. Sadly, many teachers have not been privy to the kind of support and education, in both mathematics and in the neuroscience of learning math developmentally, that the New Math demands. Furthermore, there has not been sufficient time for many teachers to become proficient with it. Consequently, New Math has fallen short of its targets but again, this is not because its curriculum is bad for kids.

The Basics + New Math = Successful Learners

In sum, I believe the solution is that students must learn their math facts but the way they learn these facts needs to change! This is because the rote memorization of facts, which is still the most common practice in North American schools, inhibits the development of number sense. Furthermore, when the New Math is not implemented as intended the fluency of math facts is often missing. This sometimes occurs in addition to a lack of number sense, which is ironic as this is what the New Math curriculum was intended to cultivate.

So... when I am asked what I think of the Math Wars, my response is always that I think we need the both the Basics and the New Math! More specifically, I believe in the strategic combination of the New Math and the Basics coupled with highly supported, well-trained, teachers who can help students developmentally understand mathematics by teaching concepts conceptually first, attaching symbols second, and focusing on the efficient learning of math facts only after the appropriate level of abstraction has been attained. This is what I consider to be the successful formula for helping all kids learn math optimally!

[pseudoreality]

Thank you for your response. My little girl is 7 months old. So it will be a little while before I will be having these discussions with her teachers, but I want to be educated about it myself when I do.

[DataDoxy]

You bet. Thanks for the question! (Got me thinking... I wonder what math education will look like when your daughter is in high school?!)

Enjoy your first Halloween with your baby girl!

[topshelf14]

There is also a side-effect to this first generation of New Math learners. There is no help/support at home. I am a "math person" so to speak and have never struggled with performing most math calculations. I do it every day at work. However, I first noticed an issue in my home life when my daughter came home with math homework (Grade 3 at that time) and I had no idea what she was doing. She was struggling and was asking me for help and I couldn't provide it. I had to ask her teacher to send me an answer key so I could teach myself first and then try to explain/teach it to my daughter. I now know how my parents felt when we switched to the metric system. Anyway, not that this response is any help to the original poster but I think educators need to realize that this is a problem with moving to a new way of teaching.

[MillerTime GFG]

Hey DataDoxy,

Had parent teacher interviews the other day for my 8 year old girl I've been talking to you about in the other thread. Figured I'd put it in here as it's math related. Her teacher suggested she go on the "LSP" program. From what I understand, there are no negatives to it, just that she gets more help. She doesn't have the basic concepts down in math and now the new stuff is piling on. (She still uses her fingers for multiplying etc.)

Just wanted to see what your thoughts, if any, are on the LSP program? I had never heard of it before she mentioned it.

Thanks.

[DataDoxy]

Hi MillerTime,

It is common for teachers to assign/use a Learning Support Program (LSP) program to kids that struggle. There are some great programs and some that are not so great... Do you know what program they are using specifically?

[MillerTime GFG]

Originally Posted by DataDoxy

Hi MillerTime,

It is common for teachers to assign/use a Learning Support Program (LSP) program to kids that struggle. There are some great programs and some that are not so great... Do you know what program they are using specifically?

I'm actually not sure. She's supposed to be sending home the paperwork soon to get the process going.

[tvp2003]

I mentioned in another thread that we have our daughter waitlisted at a charter school. Specifically, Foundations for the Future. In doing some research about the school and their philosophies, I came across this blog post:

http://michaelzwaagstra.com/?tag=fou...harter-academy

It isn’t hard to see why FFCA is popular. While regular public school administrators and school boards are largely under the sway of the latest edu-babble fads and failed progressive ideologies, FFCA encourages its teachers to use strategies that actually work.

Among other things, this means teachers take charge of their classrooms and provide lots of teacher-directed instruction. In math class, students memorize their times tables, learn the standard algorithms for basic operations, and do lots of practice questions. In reading, FFCA teachers make regular use of phonics because of its proven effectiveness. Students learn proper grammar, receive regular homework assignments, and write a lot of tests. Obviously, parents want their children to be able to calculate and read effectively.

While these traditional methodologies are very popular with most parents and some teachers, they are anathema in education faculties where teachers are trained. Education professors regularly encourage prospective teachers to be a “guide on the side” rather than a “sage on the stage.” In other words, the last thing they want is for teachers to provide a defined knowledge base and skill set to students. They downplay the importance of academic content and focus on social issues and the students’ self-esteem.

The influence of this failed ideology can be found throughout the public school system. Fuzzy math, invented spelling, no-zero policies, incomprehensible report cards, and lax discipline are only a few examples. Parents are fed up with how their neighbourhood public schools have been turned into laboratories for a never-ending succession of senseless fads. They want their children to receive a solid education, and consequently they flock to schools like FFCA.

Obviously this is simply one person's opinion, but this discussion about "traditional" versus "new" math is quite interesting to me and seems to be a subset of a larger discussion about teaching generally. Is the line as clear as this blogger makes it out to be? Is it possible to get the best of both worlds (in math, and in teaching generally)?

[DataDoxy]

This is a hot topic for sure and there are countless blogs like the one you shared where people stand firmly on one side of the issue.

For math, we know that all students can learn it but, in order to do this, teachers must ensure students understand it. Mere memorization does not promote deep understanding. Teaching conceptually first, then ensuring efficiency does.

Research tells us that traditional teaching methods (in math) only work for 20% of the population. This would NOT be acceptable if this was the stat for reading proficiency in schools but, for math people seem to be comfortable with the belief that many of us are just not "math people". Thus, the traditional way of teaching math remains the most common methodology in North American schools and the result is that many students do not learn the math they need and are required to know for the 21st Century.

My take on the debate between traditional memorization and understanding is ridiculous; we obviously need both! However, teaching math conceptually first and ensuring efficiency of facts after conceptual understanding is attained is the BEST strategy for knowing and doing math for the vast majority of learners.

[Russic]

You mention that new math is hard to conceptualize and learn when the goal is to teach (which makes total sense). My wife is a teacher, so I've seen the day to day demands placed on them, and truthfully I don't see a ton of time available for them to learn. How does something like that get rectified? Is it just a matter of needing them to teach it year after year until they find better ways?

How long has new math been in calgary schools?

[ernie]

My kids do the "new math". It threw me for a loop when that homework started coming home. I spent a week to figure it out and realized that the so called let's "go back to basics" that people so desperately want to dump the new math for is not going back to basics. It's going back to learning a process without knowing why you are doing that process. The new math is actually the building blocks and fundamentals....it's the basics. The new math is learning why you do the things you do and learning what number X and place Y actually mean rather than mimicking an algorithm.

It isn't, for example in subtraction (23-9), crossing out that two and writing a one beside the 3. It's taking a 10 from the tens column and adding that 10 into the ones column. It seems more complicated. Many more steps. But the student actually understand the basic concepts because of it. I think many people would be shocked if they went around asking there co-workers not to simply do 23-9 but EXPLAIN hat they are doing and why they are doing it. All with be able to do the former and few will be able to do the latter. The example that always goes around the internet is the 32-12 one where the person brings the 12 to 15, then the 15 to 20, 20 to 30 and 30 to 32 and adds up those increments. Yes the algorithm gets you there quicker but many will not understand fundamentally what that algorithm means or how is works.

Using subtraction again to illustrate...the "new math" or as it is often mistakenly referred to as common core is what you do when making change on a purchase. To use the example akin to a blogger I read a while ago. A customer purchases something for $5.45 and hands you a $20 bill but the register is out and no calculator is to be found. How does a person do this? They don't get a piece of paper out and perform the algorithm. you break it down into easier chunks. A nickel gets me to 5.50, two quarters to 6.00, 4 more to 10 and then 10 to 20. Ever run into a someone at a store that can't make that change to save their lives? Of course you have. And that is the reason for the new math.


Which isn't new by the way. It's how many people were taught decades ago. You know the people who are universally able to actually do math in their heads unlike a very large chunk of the people from the last couple of decades. It's what people who are good in math but went through schooling the the last 20-25 years taught themselves to do.

[DataDoxy]

Well said, Ernie!

In terms of Russic's question about how to we rectify things so that teachers are better supported to teach the "new" math, I think this can only happen when teachers are given more time and training. The fact is that most practicing teachers were just not taught how to teach math this way, nor have they experienced learning math this way. Therefore, it is not reasonable to say "implement this" and expect it will just happen without sufficient time and support, especially given all the things teachers are expected to do to prepare their students socially, emotionally and academically. We can change the text books, and the assignments but if we do not help teachers, parents, and students understand they how's and why's of conceptual math, it is bound to be fail. In terms of undergraduate programs, pre-service teachers need to be taught conceptual math before they enter the field. Post secondary institutes are currently re-evaluating what is required for Canadian (and US) teachers in terms of mathematical knowledge so they can best prepare students for learning the math they need for the 21st Century.

[DataDoxy]

Sadly, math is a gatekeeper for many kids and has been for decades. This is highly problematic in today's world as STEM (science, technology, engineering and math) is where the jobs are and will be for the foreseeable future. Students who are not literate in math and in the STEM fields will be disadvantaged in our rapidly changing, technology-driven world.

As such, math and STEM will become increasingly important in education in Alberta. This means math will be learned in a way that is not siloed, but instead will be integrated into other subjects like technology, science and art. (STEAM = STEM + Art). This means math will be taught in ways that promote a student's ability to understand and apply it to the real world in meaningful ways. Kids will need to be problem solvers and mathematical and computational thinkers. This means they will require a deep conceptual understanding of mathematical concepts and strong visual skills. Merely memorizing facts will not be sufficient.

[tvp2003]

Originally Posted by DataDoxy

Well said, Ernie!

In terms of Russic's question about how to we rectify things so that teachers are better supported to teach the "new" math, I think this can only happen when teachers are given more time and training. The fact is that most practicing teachers were just not taught how to teach math this way, nor have they experienced learning math this way. Therefore, it is not reasonable to say "implement this" and expect it will just happen without sufficient time and support, especially given all the things teachers are expected to do to prepare their students socially, emotionally and academically. We can change the text books, and the assignments but if we do not help teachers, parents, and students understand they how's and why's of conceptual math, it is bound to be fail. In terms of undergraduate programs, pre-service teachers need to be taught conceptual math before they enter the field. Post secondary institutes are currently re-evaluating what is required for Canadian (and US) teachers in terms of mathematical knowledge so they can best prepare students for learning the math they need for the 21st Century.

According to this article in the Herald, it is failing. Also, this particular elementary school (Royal Oak) is apparently bringing in a consultant (which requires fundraising to the tune of $20k per year) but it is still an issue.

http://calgaryherald.com/news/local-...algary-parents

[ma-skis.com]

Since the introduction of discovery-based math about a decade ago, Stokke says students are being overwhelmed with trying to figure out basic skills, like multiplication, which should simply be memorized.

And when they go on to more complex problem-solving, she says, they struggle, they feel defeated and then quickly give up.

I found this interesting that if they can't solve the problem multiplication, what would make someone think they have the ability to figure out a more complex problem?

I'm not saying it's not possible, but it seems like a bit of a disconnect for me.

[Traditional_Ale]

The dumber and more unequipped the populace is to deal with every day life, the more power a centralized government has.

For the record, I am a math idiot who barely survived basic remedial math in high school.

And I can school a lot of kids fresh out of high school in math, nowadays.

[Shazam]

Originally Posted by tvp2003

According to this article in the Herald, it is failing. Also, this particular elementary school (Royal Oak) is apparently bringing in a consultant (which requires fundraising to the tune of $20k per year) but it is still an issue.

http://calgaryherald.com/news/local-...algary-parents

I know all the people mentioned in that article. It's basically all 100% BS.

1) Kelly's child struggles with math in general. She was tutored at Renert, which is even MORE "new math"-y than anything the Alberta curriculum has (watch his YT videos. He's extremely progressive). I did recently talk to them about her struggles and they mentioned that she is doing better now. Also it should be mentioned that that child actually wasn't at ROE last year. So um...

2) Torres... Christ almighty. Their child did GREAT at ROE. Yeah, he's an obese brat that spews crap like "girls are awful at everything!" but let's focus on his math. He did GREAT at math! His dad was so upset though that they took him out of the school and placed him at... Renert. Great research there doofus! Surprise mother####er!

ROE did very well in the last grade 3 Alberta tests. But before anybody brags about this teaching method or that let's all realize that school test results are mostly correlated with the socio-economic status of its students.

Galileo is used at MANY schools. It is used for ALL subjects, not just math. It was a valuable resource for all the teachers. It is NOT just a "consultant" - it's a whole set of resources that the children and teachers use.

Also the fundraising was VOTED on by the people that bothered to show up for that school council meeting, so whatever.

Christ the Calgary Herald sucks balls these days.