11 The math classroom

There’s neurocognitive evidence that numbers 1-10 involve less areas of the brain than large quantities (Amandine Van Rinsveld, and others, 2017, Qadeer Arshad, Yuliya Nigmatullina, and others, 2016). It is like 1-10 numbers are more concrete as they are visible on the fingers, while larger quantities include cognitive parts of the brain that process imagination and fantasy. In the bilingual mind, also, the brain tries to adjust to the language of instruction, and tries to suppress the native language while doing math. However, in the transition to learning a different language, the native language still speaks to the individual at least to make sense of the strategies (Van der Walt, 2001). Teachers of multilingual learners may even code-switch to the native language of the learner to explain a strategy or to provide social support (Grabner, and others, 2012, Maluleke, 2019, Setati, 2002).

As a mother of a bilingual child in the United States, I developed several strategies to support my daughter into her bilingual journey through math:

• I keep with my daughter a secret “math journal” where we write colorful reminders of strategies to use. We review this frequently and come back to them when she forgets some strategy. Charts with equivalencies are also helpful to keep in this journal.
• My daughter had trouble pronouncing 30 and 40 differently. We practiced the listening and pronunciation of 30 and 40. I told her that 30 showed the tongue and 40 showed the teeth.
• When I do school math with her, I use English to pronounce the numbers and Spanish to explain the strategies. Sometimes I take her lead to provide codeswitching when she tells me the strategies she has learned in school.
• Sometimes I let her be the teacher so she explains to me math problems in English. However, this sometimes leads to evasion strategies where she diverts from a difficult topic with random playing.
• I created fun stories to introduce complex math concepts. E.g. the TENS is a frog that likes to jump always to the same ONES.
• I created an imaginary place in our study room, which is called the “palace of math” where there are certain rules. Just in this palace, she can’t sing, jump, speak baby, or talk about TV series. During short breaks, the palace disappears and there’s no rules.
• I read the direction to her in English and then translate it to Spanish. I model the first exercise as an example for her. Once I’m sure she understand the direction, I let her try on her own. If she’s struggling with the exercise, we do them together and write the strategy on the math journal.
• I desensitize her frustration by doing a brief tapping on her shoulder. I encourage her to try again. If she fails at the second try, I stop the activity. Then we take it over on a different day.
• I provide a structure where several tries follow scaffolding: the first try she does a guess; if she gets it wrong, the second try she counts with her fingers and thinks a strategy to approach the problem; if she gets it wrong, I ask her to explain how she got the wrong answer and analyze the point where the strategy twisted the result; if she still gets it wrong, I explain the way I do it and I finish the problem.
• Sometimes I teach her the method I learned in Colombia for a similar problem. I ask her to just listen to the method, not to memorize it. Then we compare it with the method she’s being told in school. I let myself get surprised by novel methods I never heard of in Colombia. While this complicates the matter short-term, I noticed that a consistent conversation about error and strategy has helped her make sense of the math much better.
• When she’s learning a strategy, I ask her to tell the number and I write it down on the paper. Once she’s mastered the strategy, I let her write down on her own. Drawing a number and thinking a strategy are two different cognitive tasks, so I try to separate them when the matter is very complex.
• I have refrained from purchasing her math video games. The reason is that school work still happens on paper. One important skill she has to work on is writing first the hundreds, then the tens, then the ones. However, I think video games, calculators, and AI provide transliteracy in finding cognitive paths to calculation. They have the potential to develop abstract thinking at a genuine abstract level.
• One day I recognized that she had to try harder because she was bilingual. She said that it was not fair to her. Then I told her that trying hard would make it gradually smarter even when short-term results don’t look like coming.

Beware of cultural assumptions

Once my daughter as given an exercise to obtain quantities out of coins and… I didn’t know the value of the coins. Recently with the reduction of cash money around, I forgot the old days of everyday usage of coins in the United States. My translanguaging strategy was to look up the coin using the Google recognition image, or just ask my daughter whether she knew. While it is definitely a nice activity to put math in context, a student may make an error because they don’t remember the coin value. Just to show my point, imagine having the same activity using Mexican currency. You would probably remain blank on how to respond to this even as adult… just because of a cultural assumption.

In this video, by minute 2:47, the creator showed the quantities of the coins, something that should be better done at the beginning and with lots of scaffolding.

Beware of global math methods!

Math may have a reputation of being universal, yet approaches to math may differ from language to language. To avoid cultural assumptions that may confuse newcomers, just be mindful of repeating your strategy in a slow manner with lots of scaffolding.

Japanese methods:

Arab methods:

French counting method:

Bibliography

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