Sami MäättäMathematics as a Language
“Mathematics is a universal language” is a statement that many have probably heard in their life. Why isn’t it taught like one?
Similarities in Teaching Math and a Language
Let’s look at some building blocks of a language lesson. This is by no means an exhaustive list, but something to get us used to the idea of drawing lines between math and a language.
- Vocabulary. In a language textbook you have pages lined with vocabulary and similarly you could say that you have vocabulary in maths. It’s the definition of the new concept, or a new formula.
- Example phrases. Next you might have pictures of talking heads that are saying phrases relevant to the chapter’s theme. In mathematics the equivalent could be the various examples where we use a new formula in different situations.
- Practising the phrases. Then you move onto actually practising the phrases. This might be that you read a phrase out loud switching up a word here and there. In mathematics these could be the easier, mechanical where some of the numbers have been changed compared to the examples.
- Discussion and improvisation. In language lessons you might then move on to more free form dicussion where you play with the language. You improvise and come up with situations where you could use the language and the phrases you just learned. Where is discussion and improvisation in mathematics? Sure we have our ‘problem solving’ and ‘word problem’ tasks, but I would hardly call them improvisation with maths.
What to Learn from Languages?
Learning a language becomes easier when you relate it to your life. That’s why I think it often starts with topics that answer questions like “How do I describe my family?” and “How do I talk about my day or my plans for tomorrow?”
I feel that in math we focus too much on repeating the vocabulary (concepts, definitions, formulas) through examples and tasks, but we forget about coming up with situations where we use, what we have learned. This also prevents the students from discussing math meaningfully and within their own context.
I hope this will spark up a conversation on why and how we teach maths. I think that discussion and improvisation in mathematics should be emphasized more.
We should have discussion and improvisation in mathematics, so we could better understand what relevance math has in our lives and also to think how you can already use your known skills in a given situation relating to mathematics.
Tasks and Facilitation to Support
How should we go about, so we can actually encourage improvisation and discussion in math lessons? This probably requires its own post, but let’s tackle it a bit here.
Tasks
- Open ended tasks: Such tasks that don’t only have one solution. Better yet: They don’t only use the knowledge you have acquired in class.
- Invention tasks: Much like open ended tasks, but students are tasked with coming up with a specific thing. For example, they could expected to come up with a way to measure the sustainability of a plastic bag.
- Malcolm Swan’s (2016.) Collaborative Learning describes many great, discussion-based approaches to mathematics.
Facilitation
- Facilitate a dialogue: As a teacher don’t pass judgment on a student’s answer, but rather encourage other students to take part in the discussion. Phrase like “Sounds interesting. X, what do you think of Y’s idea?” gives more power to student discussion.
- Don’t ask questions which you answer yourself or are just looking for another student to answer correctly. Instead always give time to talk about in pairs, or small groups and then gather answers afterwards.
Inspiration for the Post
This post was partly inspired by the article Learning the Language of Mathematics by Robert E. Jamison and by my own experiences learning German and teaching Finnish part time in Germany.