See also – about maths at World’s End
An important aspect of teaching for mastery is encouraging the children to record their understanding of each concept via jottings in their maths journals. This work is independent. Below is an example of how different the children’s work looks compared with how it used to look. Both work samples were from year 3 children who achieved a level 3 at the end of KS1.
|Work Sample: September 2015||Work Sample: September 2016|
|A typical activity under the previous style of teaching. The same procedure repeated many times. The child was considered high attaining so was accelerated into 4 digit number.||After a lesson exploring place value, the child was asked to journal what they now understand. This child demonstrates an understanding of how to represent the number 327 as base 10, bar model, two different part whole diagrams (same value different appearance), as a number sentence and as words. There is much more evidence of a depth of understanding of place value.|
Depth through multiple representations
The journals allow us to see the depth at which the children have understood the work. The class is taught together but the different depths of learning can be seen in the journaling.
A year 3 lesson – subtraction with re-grouping
|When asked to journal what he understands about 435 - 268, the child demonstrates that they have begun to understand the column subtraction. We know this due to the way that they have partitioned the part whole diagram. They have understood that to complete the first step and subtract the ones, they must regroup the 435 into 400 + 20 + 15.||This child completed the same introduction to the lesson but the journals show us that they understood it much more deeply. They have drawn the Base 10 to show how to regroup, they have completed the written method, they have drawn all three part whole diagrams which demonstrates an understanding of how the numbers are partitioned at each stage, and they have represented the calculation with a bar model along with a sentence stem from previous learning of addition, this shows us that the children understands the relationship between addition and subtraction.|
To take learning deeper, we use variation theory and the advice of Dr Yeap Ban Har, Advisor to the Curriculum Planning and Development Division of the Ministry of Education in Singapore and Debbie Morgan (Director for Primary: NCETM)
Precise Use of Mathematical Vocabulary
Precise use of mathematical vocabulary used in lessons can be seen reflected in the journals. For example, this year 3 lesson on division.