Think about this question: ‘Express 75 as a product of its prime factors’.
Many students are unable to answer questions like this in a test situation, despite having successfully performed similar tasks many times in class and often having revisited the topic in several different years. There are many reasons for this, but the language of the question itself is often the main barrier. Interestingly, it is not just the highly mathematical words like ‘product’, ‘prime’ and ‘factors’ that cause problems. A significant number of students struggle with the command word ‘express’ and get no further.
Tiers of vocabulary
In their 2017 book ‘Bringing words to life’, Isabel Beck et al. talk about three tiers of vocabulary:
Tier 1 – basic words with a single meaning that we use in everyday talk such as girl, book etc.
Tier 2 – high frequency words that occur in many areas, but are less common in everyday talk such as apply, explain, verify etc. These words may also have more than one meaning.
Tier 3 – less common subject-specific words such as numerator, equilateral, decagon etc.
It is important for us, as teachers of mathematics, to make sure our students gain familiarity with the Tier 2 words as well as the Tier 3 (that we often list as the ‘key words’ in our lessons). Alex Quigley, a Senior Associate at the EEF, talks about helping students ‘breaking the academic code’ to help them access the curriculum, citing the ‘vocabulary gap’ as a major barrier particularly for disadvantaged and EAL students. He also notes that students need to meet a word between four and ten times before they internalise it. This should make us reflect on how we deal with vocabulary – we might think we spend considerable time defining and working on a word when we first introduce it, but if we just assume it’s ‘sunk in’ thereafter we might be doing our students a disservice.
This is especially important in mathematics as there are so many words that have meanings in maths, but may be already familiar to students from their meanings outside the subject. Here are just a few examples:
Talk, talk, talk
Many (if not all) of the tasks we suggest at WRM are designed to be the basis of classroom discussion. The more often students get to engage in mathematical discourse, the quicker their understanding of Tier 2 and 3 words will grow. Take this question from our Year 7 scheme:
The above is an example task from our Year 7 schemes that encourages discussion.
Listening to students’ discussion is a powerful assessment for learning tool, enabling teachers to really understand what students know and don’t know about a topic.
We also recommend the specific discussion of vocabulary through models such as the Frayer model:
Rather like goal-free problems, when students work in pairs or groups to find their own definitions etc., it’s not the answer they produce that is important, but the discussion round it that deepens their understanding of the word or concept involved. In particular being able to distinguish between examples and non-examples – things that are close in meaning but not quite the same – really enhances understanding. The more opportunities we create for mathematical talk, the more chances there are for students to get to grips with mathematical language concepts, and the better their learning will be.
Beck I, McKeown M & Kucan L (2002) Bringing words into life
Quigley, A (2018) Closing the vocabulary gap
Hattie J, Fisher D & Frey N (2017) Visible learning in mathematics