This is the second in a series of posts about literacy in maths. I mentioned in my previous post that this post would explain more about tier 1, 2, and 3 words and also include some further analysis in relation to the higher tier papers.
If you are looking for a place to start in relation to the instruction of vocabulary, I would suggest the book, “Bringing Words to Life” by Beck, McKeown and Kucan. There are lots of important ideas in this book but one of the most widely discussed is how to choose which vocabulary words to teach. Basically, they divide words into three groups, or tiers, of words in terms of the words’ commonality (more to less frequently occurring) and applicability (broader to narrower). While the term “tier” suggests a hierarchy, a sort of ranking of words from least to most important, in reality, they suggest that all three tiers of words are vital to vocabulary development, although learning tier two and three words typically requires more deliberate effort than learning tier one words.
The “tiering” they suggest divides words into 3 broad categories:
Tier 1 are basic words that occur frequently in everyday life/speech and are not considered to be a challenge. Beck argues, that such words generally are not worth teaching explicitly, as they will be absorbed via continued exposure. This will include words such as cold, warm, fire, cat etc.
Tier 2 are words which occur across a range of subjects and are more likely to appear in written work rather than speech. The thing with some of these words is that their meaning can vary depending on the subject and context, for example “analyse” can mean different things in English lessons and Maths lessons and this is why they have become a focus area for lots of schools – they are vital to understanding what an exam question/text means. A good example that I came across when reading around this subject that made me go “ahhhh … got it!” was the word “relative” … students will probably know the meaning in terms of a family member but not when used within maths when used in say, relative frequency.
Tier 3 words are subject and most of us will know what words students won’t know and typically they are unlikely to come across them in other subjects. Knowing which words, we need to explicitly teach within our subject is an absolute no brainer for me – they often have a fixed meaning and very often they are key to understanding when introducing a new topic and so, for me, they are closely linked to subject knowledge. Words such as: Trigonometry, addend, numerator, trapezoid etc fall into this category.
There is no specific rules or magic formula for placing words into tiers and it’s important to note that words can also fall into more than one tier. Much of the research suggests that tier 2 words are critical to building literacy skills, and so it is important that we emphasise them in our teaching … BUT does giving a word a label as a specific tier help us … probably not! The thing (I think!) we need to do is to consider any words that appear in questions we are using in lessons (we are after all professionals!) and consider whether or not they will require an explanation … if in doubt ask the students to explain what a word means and then if required, use your chosen strategy to explain it further.
For those of you with my level of patience, I’ll give you the short version:
- We don’t need to worry about Tier 1 (Basic vocab) – students should arrive knowing the basics and will quickly pick these words up in conversation.
- Most teachers will be aware of which subject specific words (Tier 3) students won’t know and teaching the meaning of these will be second nature to many of us. If its not … it should be!
- Tier 2 are high frequency and /or multiple meaning words and this is where we could have a problem, because we, as teachers/adults are familiar with these words that we need to make sure that we notice whether or not pupils know them.
NOW TO BE A BIT CONTENTIOUS. I genuinely believe that Mathematical vocabulary is an important, but over-looked aspect of learning mathematics and it can be a barrier at key stage 4 especially with the greater need for students to read and understand worded problems in the 9-1 GCSEs. I do think that a student’s linguistic (is that the word I’m think of!?!?) ability will have more of an impact on their performance than previously. Whilst all that I have written above is a starting point we cannot forget that Maths is a language in its own right, but unlike most other languages, we do not read it solely from left to right, but also from right to left, top to bottom, bottom to top, or a combination of these directions. When writing mathematically we use numerals AND symbols – the use of these symbols means that we have to “translate” these not just into their precise meaning but also in the context of the mathematical statement that they are contained in AND then we have to do something with this information to solve a given problem. Its not as simple as teaching the definition of words to students … literacy in maths is complex.
Not only is it complex in the classroom, the implications in terms of assessments is far reaching – in my reading around literacy in maths I also came across a paper by A. Kan, A. and O. Bulut,(2015) called ‘Examining the Language Factor in Mathematics Assessments‘ and they found that changing the language used in mathematics questions affected student performance. For example, if numeric questions were converted into worded questions, students’ performance worsened if the language became technical, but improved if the language became more commonplace.
Despite all of the above its important that students at least know what the common command words they are likely to come across in their GCSEs. My previous post included the analysis I’ve done for the foundation tier and below I share the same information for the higher tier.
The below table shows the frequency of the command words found on the Pearson/Edexcel Summer 2019 Higher papers:
From this I have produced a word cloud which you may want to use as a poster:
The below table shows the frequency of the command words found on the AQA Summer 2019 Higher papers and as per the Foundation papers you will notice a high incidence of the word “circle” as this relates to the multiple-choice questions:
Again, from this I have produced a word cloud which you may want to use as a poster.
I have also pulled both lists together below (in alphabetical order) that puts the word frequencies against each other:
As always, I will leave you to draw your own conclusions and I hope some of the above has been useful!
PS: I have saved this analysis and posters in the grade boundaries & data folder in the essentials tab of JustMathsOnline for those of you that have access to it!