Thread by @mathsmrgordon

Thread:
If you haven't read "Is it true that some students just can't do maths?" by @danielwillingham yet then I'd really recommend it. Some thoughts on it to follow 1/n
aft.org/sites/default/…

2/n humans are born with an ability to appreciate space and number and their relationship to a degree.

3/n 10 month old infants can appreciate the difference between 1 and 2 but are less effective at judging between 2 and 4. Thesis monkeys outperformed infant humans in this aspect.

4/n a study showed that 70 % of the time, left eye monements related to subtractions and right movements to addition with a brain scan

5/n humans were quicker to identify even numbers when they were small and odd numbers when they were a little larger by pressing 1 of 2 buttons

6/n we learn to count and th ebilitybto dnumerate beyond around 4 is dependant on the culture specific system and language.

7/n The Mundurucu, Amazonian indigen group only have words for numbers up to 5. Beyond this, they refer to quantities as “many.” Their sense of number is also not linear. Representing 1 to 10 on a number line shows more spacing between 1 and 5 and more crowding between 6 and 10

8/n Americans were able to perform the same task with equal spacing but both groups performed similarly for larger number lines e.g 10 to 100

9/n unsurprisingly knowledge can be separated into factual, procedural and conceptual. He refers to “math wars” between trads and progs but states there is evidence both ways for procedure vs conceptual sequencing. The aim should be to teach “both in concert to aid comprehension”

10/n conceptual understanding is more difficult to attain. Careful thought to manipulatives should be given. “Manipulatives themselves are abstract... they can actually impede learning.”

11/n he put these impediments down to i) the manipulatives at times being aesthetically distracting from their purpose ii) their relationship to the concept being obscure

12/n studies show that students don’t understand the base ten system and less than 25% of students understanding the equals sign - the big problem being that students see this as a queue to write an answer

13/n “concreteness is not a magical property that allows the pouring of concepts into students heads.” It’s the familiarity of manipulatives and analogies that help because it “allows students to think in new ways about things they already know.”

14/n as well as familiarity students should be given opportunities to compare lots of examples. These comparisons should be made explicit otherwise the examples effectiveness decreases.

15/n what does this mean for teachers?
1. Ensure analogies and manipulatives can be transferred and are flexible. Consider dependant future topics
2. Cultivate conceptual knowledge but don’t sacrifice factual and procedural knowledge

16/n
3. Ensure students gain automaticity with facts and procedures through regular practice
4. Choose a curriculum that develops conceptual development by
a) studying less concepts in more depth
b) sequence content so that the mental gap between concepts is small

17/17 don’t let students say “I’m no good at maths” without challenging it. Almost all students can learn maths to secondary school level. Support, persistence, effort and time are the key variables.

Thread end.