Monday, June 22, 2015

Meet the "New Math"...Same as the "Old Math"?

The title is partly flippant, but mostly a music geek's Who reference ("Won't Get Fooled Again"). We spend a lot of time debating "new" math reforms (that are in some cases over 50 years old), and we spend a lot of time thinking about the things that are "old" (time-tested, essential, or that truly matter). Where we stand on these issues says a lot about our own beliefs as educators, and things we learned and internalized in our own schooling.

I honestly thing we need to focus on the common ground that we all share in our beliefs about math teaching and learning. Polarities like "new"/"old" and "discovery"/"traditional" don't tell the truth about how things actually are.

What follows is a short module designed to get us examining our own assumptions about math teaching and learning. Its purpose is not to inflame. Its intended audience is anyone who cares about math teaching. If that is you, please feel free to comment.

Meta moment: the text below is also in this Google doc if you want to add to it:

On “Back To Basics” vs. Reform Mathematics in Schools

The debate over what constitutes “good” math instruction has flared up again recently in Alberta, with the publication of a recent CD Howe institute report, which gives recommendations.

Questions we all must answer for ourselves, as mathematics educators:  

  1. What do we mean by “basics”?
  2. What factors have influenced your own personal definition of the things that are “basic” to math teaching and learning?

Further to #2, reflect on your own personal experiences with school math. To a large extent, your answer to the question “what is math?” was informed at a young age by your school experiences.

3.  Did you see math as creative, vibrant, beautiful, interesting and alive as a student?

4.  Does it matter whatsoever if you experienced math as creative, vibrant, beautiful, interesting and alive as a student?

“Discovery” Learning: What does that mean?

What, if anything, do we mean by “discovery” learning?

See if the Wikipedia article helps us here.

Here is an article that seems to be the main one used as fuel against “pure” discovery learning. (Or, learning that is done with minimal teacher guidance).

In your opinion, what are some math concepts that can be “discovered” through exploration, and careful teacher guidance.  

I will give your the relationship between any circle’s circumference and its diameter. What can you give me? (Examine Ontario TIPS unit here.)

A lot of time has been spent unravelling what we mean by “direct instruction”, “explicit instruction”, and “inquiry learning”.

Is “guided discovery” the same as “direct instruction”?

As a teacher, what is your own personal definition of direct instruction?

Here is John Mighton, founder of JUMP Math, on what he sees as “guided discovery”:

Fluency, Automaticity, Memorization:  3 Sides of the Same Coin?

My assumptions:
-more practice with more number facts will lead to being fluent with them
-encountering number facts frequently through meaningful work, problems, and games will lead to them being committed to long term memory
-flexibility with facts, gained through things like number talks, will lead to more connections being made between numbers, and facts
-K-3 is a time to build a deep base with number sense
-teaching through problem solving, as specified by the Ontario Curriculum, is the best way to build procedural and conceptual understanding
-direct instruction does not always mean talking to the whole class at the same time
-mini lessons on key mathematical concepts, given at a key time in the instructional sequence, pack the most punch

Assumptions that are often made by “back to basics” advocates:

-number facts should be committed to long term memory ASAP, to “get them out of the way”. Grade 4-5 for memorizing times tables, for example, is seen as far too late
-standard algorithms should be taught as early as possible
-encountering problems without prior scaffolding is too much of a cognitive load on students
-forcing students to explain their thinking gets in the way of actually doing math
-direct instruction should take up most of our time.

Here is a Jo Boaler article on fluency that is popular right now:

Develop your own list of assumptions. What common ground do you see? What things do we all agree on?