Teaching Mental calculation Strategies for improved number

sense: A cognitive neuro-scientific approach

ROSELLE HANSEN-HANEKOM

What we already know in education

You need Number sense to do Mathematics.Teaching mental calculation is the best way to go about it.

(Graven, Venkat, Westaway & Tshesane, 2013).

Mental mathematics plays an important role in the curriculum.

(CAPS Foundation phase– DBE,2012:12)

10 minutes every day

Cognitive neuroscience: helps us to better understand how the brain naturally learns Mathematics

Flow of knowledge in the brain (Zambo & Zambo, 2008)

Sensory Cortex Concrete experience – use this part of the brain when making use of counting strategies to

calculate answers

Integrative Cortex1. Connect new knowledge with what they

know and understand.

2. Involves emotion – block or enhance memory

Motor cortexTo create long term memory the brain needs action:

role play, real life situations, dancing, singing and also writing tests.

Key concepts needed to do mental calculations:(Menon, 2010:516)

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1. Understand numerical properties(In as many different ways as possible - Sousa, 2016:30)

Activities:1. Skip counting2. Up and down the ladder3. Chain questions: Start with 135 add 7. This is

142. Now take 3 away, that’s 139 and add 10 etc.

4. Bonds: Counting

Strategies

Effortless retrievalBaroody & Rosu, 2005)

Traditionally Asian children are better at Mathematics.

Evidence suggests this is because of their language and the way they count. In English it is difficult and don’t express the value of the number

(Sousa, 2016:87)

New idea: one two three four five six seven eight nine Ten

Ten andone

Ten and two

Ten and Three

Ten and Four

Ten and Five

Ten and Six

Ten and Seven

Ten and Eight

Ten and Nine

Two Ten

Two Ten and one

Two Ten and two

Two Ten andthree

Two Ten andFour

Two Ten and Five

Two Ten and Six

Two TenAndSeven

Two Ten and Eight

Two Ten and Nine

Three Ten

Three Ten and one

Three Ten and two

Copy right: 2015 by David A Sousa. How the Brain Learns Mathematics

Do you think learning to count, making use of a hundred chart is brain friendly?(Sousa, 2016:87)

2. Fact retrieval and calculation

The better the memories created the better learners’ fact retrieval will be. If there is no memory when doing calculation, they need strategies to help them do their calculations.

(Menon, 2010:516)

Bridging through 107 + 5 = (7 + 3 )+2 = 10 + 2 = 12

Doubling: 7 + 5 = 2 + 5 + 5 = 2 + 10 = 12

Compensation: 14 – 9 = 514 – 10 = 4 but 9 is one less than 10

Baroody, Cibulsksis, Lai & Li (2004)

3. Complex Mathematical computation(Menon, 2010:516)

Only when the first two stages are reached will learners be able to more complex calculations:

45 + 13 = 40 + 10 + 5 + 3 = 50 + 8 = 58

■ Working memory – load as low as possible problem solving

■ Attention■ Visuo-spatial processing

Less is more….Shorter is better….AGE

(IN YEARS)AVERAGE CAPACITY AND

RANGE (IN CHUNKS)AVERAGE TIME LIMIT

(IN MINUTES)

Younger than 5 1 to 2 No reliable data

Between 5 and 14 3 to 4 5 to 10

14 and older 3 to 5 10 to 20

“Chunking” increases the capacity of the working memory:3 + 1 + 1 = 3 + 2 = 5

10 minutes = change

What else does cognitive neuroscience bring to the table that is new?

All learning has an emotional basePlato, 2000 years ago

Emotion shapes and is shaped by cognitive processing

Hinton, Miyamoto & Della-Chiesa, 2008:88).

Emotion drives attention and without attention no learning can take place

Sousa, 2008:100

Decoding 2 + 3 = 5 takes place in the sensory cortex, but it is the affective network (emotion) that has a major influence on cognition or the motivation to understand.

Extrinsic motivation

•Punishment/reward•Short term•Feel in control and

competent

Intrinsic motivation

•Feel in control of learning -Understand beliefs and goals

•Joy

Amotivation

•No connection between own needs and teacher’s

•Autonomy, competence and social belonging

Motivation (Orhan Őzen, 2017:36; Liu et.al.,2017:6)

Autonomy Neuro Plasticity – Make yourself smarter

(Willis, 2006:3)

Brain develops new pathways - adapt to new information from the environment.

For teachers: Present material in as many ways possible to encourage more connections to form in the brain.

Practice makes perfect.

Practice does not make it easier – it actually changes the brain.

Competence: Neurogenesis and pruning

(Willis, 2006:1)

Learning causes the brain to growBrain need to be pruned to improve

For teachers: Learners need to interact regularly with new knowledge until solid foundation is formed then touched on every so often to ensure it stays accessible.

Social belonging - No “acting out”Create an environment where learners feel save enough to take risks and not feeling embarrassed by giving incorrect answers.

(Penlington, 2013:18)

Fear conditioning (Hinton, Miyamoto & Della-Chiesa, 2008:91)

For teachers: Make use of feedback of test to show that it is NOT only about the answer but more about WHY you made a mistake and how to fix it.

Teacher EQ - Take care of yourselfAccording to the Norms and standards for educators (DOE, 2000), a teacher is seen as:a leader, administrator, manager, scholar, researcher and lifelong learner who also have a community, citizenship and pastoral role.

1. Recognise your feelings2. Recognise the feeling of others3. Motivate yourself

What makes you happy? What make the learners happy? How can you use that?

4. Manage your own emotionsYou need to be calm and in control of your emotions

5. Positively impact with othersLearners who feel that their teacher takes their needs into consideration will react positively towards her and the learning.

(Fleischmann:2018:59)

Lesson planning

Memory compatible 10 minute chunksPrimacy regency effect Prime time to learnCognitive closure Re-capPractice SocialisingWriting Test, homework etcDIFFERENTIATION (Sousa; 2016)

Different types of intelligences:Word smart Need discussionsLogic smart Need proofPicture smart Need maps, graphs etcMusic smart Sing a song, rapBody smart Need movementPeople smart Need interactionFeeling smart Need emotional expression- I liked..Nature smart Find patterns in nature

(Sousa, 2016:68)

FIBONACCI NUMBERS

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