Teaching Maths for Mastery
Maths curriculums all over the world often emphasise the importance of developing learners mathematical fluency, conceptual understanding and reasoning skills. These skills are not always easy to assess. Cue the humble maths journal.
Maths journals are an important part of a maths mastery approach to teaching. For those new to maths mastery, you might be wondering, what is a maths journal?
Let’s lay out the basics.
Maths journals are an exercise book — grid, lined or plain paper — used by learners to record their methods, explanations and ideas for solving maths problems and learning of mathematical concepts.
Maths journals provide teachers with insight into a learner’s thinking and understanding of mathematical ideas, allowing them to assess and address misconceptions as they surface.
Every journal entry needs to begin with the date and a title.
Often in maths, we begin the lesson by letting children know what mathematical concept they are going to learn that day. We give them the learning intention or the ‘We Are Learning to’ (WALT) to record at the top of their page.
A journal title is similar to a WALT but instead of telling learners the mathematical concept, the journal title comes from the learner and will reflect what they think they have been learning during the lesson.
However, we can’t expect learners to just know how to write a journal title. We do need to model and make them aware of what we expect. A good journal title should reflect the mathematical idea the lesson has focused on. Journal titles offer insight into a learners level of understanding of the concept.
Take the following maths journal title examples from Maths — No Problem! NZ Textbook 2A, Chapter 7, Lesson 6 (the Explore task).
If a child’s journal title for this question is:
Journaling follows the structure of George Polya’s research:
“It is better to solve one problem five different ways than to solve five different problems the same way.”
Learners are typically given one problem or mathematical idea to journal about.
Don’t put too much focus on whether your learners solve the problem. Let journals show you how your learners express their mathematical thinking. Encourage your class to use different types of journals to show their understanding of mathematical ideas.
Journals can be used almost as a diagnostic tool for both learners and teachers. When journaling at the beginning of the chapter, learners may record what they already know about a topic, giving an indication of their starting point.
Learners may journal a number of times throughout a unit of work. These journals may reflect different methods, representations or discoveries they have made to explain their understanding of concepts.
Journaling can be used at the end of a topic as an assessment tool — recording what the children have learned. It can often be interesting for learners and teachers to compare journals at the beginning of the unit with journals at the end of the unit.
Learners should be encouraged to articulate and explain their thinking using written explanations, diagrams and numerical representations in their journals.
Here’s an interesting maths journal prompt. As mathematical ideas become more complex, words will not always be the most effective way to articulate information, journaling can provide an opportunity for learners to develop the ability to present information verbally, numerically and visually.
Mathematical language is an important part of being able to understand the abstract symbols we use in maths to represent ideas. Journaling provides learners with an opportunity to explain their understanding of concepts using mathematical vocabulary, taking learning deeper. Why not keep this maths journal prompt in mind for your next lesson?
The more learners journal, the more beneficial it will be for them. Daily journaling develops children’s metacognition skills. It encourages them to reflect on the mathematical concepts being learned and how to best articulate their thinking.
If you’re new to the mastery approach, journaling is a practice that can increase in frequency as learners become more familiar with the learning style. Mastery style lessons are often far more robust than how learners may have previously been taught, if they have come from an ability group setting.
Many teachers find it difficult to fit journaling into every lesson at first, so they will gradually increase the frequency of journaling as everyone becomes more confident and familiar with the lesson content and structure.
Maths journaling can be unstructured and there is really no ‘right way’ to do it. But following these journaling fundamentals will ensure learners develop a deeper understanding of mathematical concepts.
See how Maths — No Problem! can support your practice through award-winning textbooks and workbooks, step-by-step teacher guides, and online CPD videos.
Teaching Maths for Mastery
