Research and Results to find a better way of teaching Mathematics

We talked about the brain and mathematics and our present performance in the teaching of mathematics. This week we talk about research. More specifically the RESEARCH PROJECTS that started formally in 2000.

Projects: All projects have a start and an end. They are ONCE OFF activities. It is ESSENTIAL to define the OBJECTIVE of the project BEFORE starting: It MUST be defined in MEASURABLE OUTCOMES.

Most projects concentrate on activities but are short of MEASURABLE OUTCOMES.
Name of the project: SYFERFLUKS! Freely translated it means: Being diligent with numbers.
Perhaps DILIGENT DIGITS is an appropriate translation.

Eventually, it morphed into Towermaths. But that is only in 2014.

The Measurable Outcome of the Syferfluks project is defined as:

To have improved grade R and Grade 1 results in mathematics in at least two major Quintile 1 schools such that 80% of learners score 80% or more in the tests of the department of Education.

Mathematics is NOT like other subjects. It is NORMAL to score 100% in Mathematics. This is because there is only ONE correct answer.

More important: To score 50% (the current pass standard) in mathematics results in an even worse result in subsequent grades. There is no such thing as knowing half of mathematics just as it is impossible to have half a baby. It is ALL or NOTHING!

Research: There are two options:

  • Design an alternative method of teaching mathematics and test it on a representative sample of learners. NOTE: This is NOT an alternative curriculum. It is a better methodology in teaching mathematics. Normally this involves TWO similar groups of learners. One group that is subjected to the new methodology and another group (the so-called control group) that uses the present methodology.
  • Start with a clean slate. Assume I am from MARS and study the behaviour of pre-school infants of the human species by OBSERVATION. I call this the Jane Goodall model. She simply studied the behaviour of chimpanzees WITHOUT ANY PRECONCEIVED assumptions or TRUTHS!

ACTION Research: Because of my background and experience in Action Research and because it seems more suitable I chose the second option - studied the behaviour of pre-school infants WITHOUT ANY PRECONCEIVED assumptions or TRUTHS!

While starting my research on the behavior of 4+-year-olds, I also had to solve the problem of outdated mathematics.

That was the easy part. After only 4 years the following solutions had been created, designed, and manufactured at a cost within the means of a typical rural school.

We also developed some learning aids such as:

  • ·         Number chart
  • ·         Tower
  • ·         Multichart
  • ·         Algebra game
  • ·         Street soccer

These learning aids (tools) are designed such they can ENABLE a typical Grade 1 learner to:

  • Add a number of 2 digit numbers of which the sum is less than 109. This includes examples like: 21+33+55=109.
  • Subtract numbers within the range of 0 to 109 with a remainder. 98 – 63 – 24 = 11
  • Add and subtract numbers such that the result is within the range 0 - 109. Example: 22 + 17 – 15 + 63 = 87
  • Multiply ANY two numbers with a product less than 109: Example: 3 x 29 = 67
  • Divide numbers with a teller less than 109. This includes 91 ÷ 18 = 5 remainder 1.
  • Use letters like a and b for unknown numbers and add a + b = c when a and b are in the range 1-6 and a and b are random numbers.
  • Use negative numbers in a street soccer game.

 PROVIDED MATHEMATICS is INTRODUCED in HARMONY with their ANALOG BRAIN.

To solve that problem took the best part of 12 years.

First I had to explore/discover their world through patient observation.

This is MOST important because anything NEW MUST build on PRESENT KNOWLEDGE and PRACTICE (Judy Willis). The following picture emerged:

  • They live in a geometric world.
  • Their brain separates meaningful signals from meaningless noise. This is probably the most significant property of an ANALOG brain.
  • They learn by FAILING FORWARD. This is driven by ACTION and IMMEDIATE FEEDBACK. If we were sanctioned/ridiculed/spanked every time we fell down on trying to walk we all would still be crawling.
  • They learn by playing. Their attention span is infinite when playing.
  • They know hundreds of words.
  • They can express their opinion and needs.
  • They manipulate their environment to their advantage
  • They know hundreds of objects by name and know their place and purpose in their environment.
  • Many speak more than one language fluently
  • They have a rich imagination.
  • They have limitless curiosity.
  • They survive against all odds.

 

This is hardly new knowledge. It is still VERY IMPRESSIVE.

Perhaps just as important is to know what they do NOT do.

  • ·   They do NOT count things.
  • ·   They do NOT give up UNLESS discouraged.

Research in the first 12 years was anecdotal. One on one OR at best One on TWO or THREE.

ALL of the expectations were realised with the majority of learners.

All research and product design and development up to this stage is entirely financed by myself and my wife.

2013: My first pilot project was at rural Ruiterbos Laerskool. (70+ learners, 4 teachers) It was financed by Drs. Bert Buiten and his wife Drs. Susan van der Reeden of the Netherlands. Both of them are still involved in Towermath.  Susan is the principal of a major Christian Teachers College. In 2019 she sent five students to assist with implementing TM in a number of rural schools in the Eastern Cape. The results confirmed the promise of the TM methodology.

2014: My second pilot project was at Isalathiso Primary School. It involved 1 grade R, 1 grade 1, and 1 grade 2 class. This project was done with the support of Mrs. Heloise van der Merwe. This project was entirely financed by myself. On her retirement in 2017, Heloise became the heart and soul of Towermaths.

The results exceeded all expectations. A number of demonstrations to the Western Cape Department of Education ignited a hesitant level of interest.

2017-2019: Pilot projects are completed at Hartenbos Laerskool, Garden Route Primary, and Isalathiso Primary.

These are sponsored equally by African Rainbow Projects and SANLAM.

But that is part of next week’s story.

Prof. Koop Bullinge


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Towermaths - The breakthrough in understanding Maths.  


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