Inequality is a Waste We Cannot Afford

We are all aware that minorities are underrepresented in STEM fields in the US — they earn only 12.5% of all such degrees, although they make up nearly 40% of the population. (link here)  Women make up less than a quarter of those working in STEM occupations, and representation of women of color is even lower, with Hispanic, Asian, and African American women each receiving less than 5% of STEM bachelor’s degrees in the USA. (link here)

This is not only unfair, it is a huge waste. There are geniuses,  potential creative mathematicians and covertly competent students falling through the cracks of our educational system daily, with their lives’ contributions and fulfillment squandered. There is debate about the root causes of this loss – poverty, racism, low expectations, feelings of isolation. All of these matter, and the loss is huge.

It doesn’t stop there. Many children from every socioeconomic background learn to dislike and avoid math in school.  In fact, even adults working in STEM fields today (including some math professors) describe their near-failure in math classes in school and college, before something turned it around  –  an inspirational mentor, a role model, luck, or stubborn perseverance. (see examples in this Quora feed and this NYT article).
What are we to do???

Pathways to Change

“The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.”
~ Paul Lockhart

1.     S-L-O-W Down.

We have lived in or visited countries that teach a curriculum significantly less crowded than ours. Singapore, Finland, Germany, Canada – all teach fewer units a year yet score higher on international testing. (Pisa 2018 scores here) Finland has higher scores and a greater equity of scores, even among immigrant language learners.

Slowing down means longer units, more depth, and less memorization. We campaigned long and hard for this change in our own school’s curriculum. (See our earlier blog here: “Slow is the New Fast)

2.  Use Manipulatives. Every Day.

In our own anecdotal experience (still… >60 years combined!), about one third (!) of all students are visual learners, and therefore do poorly with the traditional ‘memorize and move on” approach to math. These children need three times – four times – eight times — as much time at the concrete level as we’re currently giving them. When not given enough time, these students give up, try to memorize long enough to pass a test, and label themselves as lifelong failures at math. Yet – given the time they need – they do learn math, all the way through high school math and beyond. We’ve seen it over and over. Whether they are girls, minorities, English language-learners, or have learning differences — they CAN learn math, given time! We cannot write them off as failures, or torture the love of math out of them with incomprehensible drills. (see our website for lesson plans – 4th/5th/6th grade – that incorporate manipulatives in virtually every lesson.)

Verdict: Less is more. Slowing down and teaching Concrete >  Pictorial > Abstract allows students who would otherwise struggle and dislike math to succeed.

3. Teach With Challenging Questions.

Whoa! Isn’t this a contradiction to points #1 and #2?
Not at all.
By slowing down and using manipulatives, we can switch to a problem-based curriculum that engages and builds long-term,  conceptual understanding.
Try the 2nd grade question at right. It’s not as easy as it first looks! Yet, given blocks and time, virtually all our 2nd graders can solve it.
(PS: the answer is not 33)
(PSS: click here for an explanation, but try it first!)
Did you notice? This is a problem that encourages
(a) procedural, mathematical thinking
(b) use of manipulatives and language as the underpinning of procedural thinking, 
(c) Equity – This problem is accessible to any child with blocks and perseverance —  and
(d) it’s fun, especially in pairs/small groups.
Teaching for equity does NOT have to “water down” the curriculum.

Final Verdict: All it takes to grow students who make good progress in math is

  • Manipulatives,
  • time,
  • and a respect for the intelligence and curiosity native to each human.

We are problem solvers by evolution. Our brains seek out patterns, we use experimentation and observation and distill meaning. We create art, music and poetry to express the wonder we feel at our natural world.

Mathematics is a quintessential human art form, and should be taught with the curiosity,  patience and guidance it deserves.

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