# Supporting the 4 components of learning Maths

Early exposure to numbers and counting is just as important as exposure to letters, words and reading. Asking a child how old they or can they count to 5, just confirms that they’ve learnt the answer to those questions. It doesn’t necessarily prove that they understand numbers and quantity.

Think of the subject of mathematics as building a house…. foundations (concrete stage, fundamental skills), walls (semi-concrete stage) and roof (abstract stage). Math is a complex subject….if foundations are not solid, the rest of the house will be full of cracks. Often kids with severe Math challenges, remain on the concrete level and cannot move to the next stage.

There are 4 corners/pillars/components that “mathematics” is comprised of:

1. Learning and Recalling Math Facts (bonds and tables),
2. Learning and Using Math Procedures (operations),
3. Understanding Math Concepts (incl. vocabulary & topics such as measurement, time, working with money, etc. and
4. Math Problem Solving (word sums)

Some of the challenges that have been identified in children who struggle with Maths are found within each of the four components:

#1 Learning (and recalling) the Math facts:

A child:

• Does not have a strong sense of numbers and does not understand that there are basic patterns in numbers…i.e., 2+3 = 5 and 3+2 =5, or struggles to learn skip-counting and place value.
• Is inconsistent, remembering some math facts while forgetting others (memory and attention play a big role).
• Has difficulty remembering multiplication, division, and/or other facts while solving problems (working memory).

Supporting the primary school child:

• It is important to learn to recognize and read number names and symbols. Abstract number symbols must be linked to the number names for the child to see, so it might be necessary to first show the actual object, next show the picture of the object initially for smaller kids to correlate….otherwise counting becomes rote with little to no understanding…and this may cause difficulty in understanding what is required.
• Have real objects or counters available. Don’t expect them to count in their heads or calculate in their heads if they aren’t there yet.
• Encourage them to use number grids, number lines, times table grids (crutches) but always go back to the real object if this is more helpful.

Supporting the high school student:

• Make use of tips and tricks, mnemonics, raps…consult YouTube. 11, 22, 33, 44 etc.
• Using the commutative property in addition and multiplication,
• Using a strategic approach and start with what you know, “I don‘t know 7 X 6, but I do know that 7 X 5 = 35, so one more 7 makes 42; or I know that 7 X 7 = 49, so one less 7 makes 42.”
• Be aware of the impact of attention and memory – don’t do Math homework late at night.
• Encourage self-checking with a calculator.

#2 Learning Math procedure/operations:

A child:

• Struggles with the methodology…struggles to remember the steps in a sum i.e., long division or multiplication.
• Struggles to remember the rules i.e., rules for working with fractions, rules for solving equations, etc. and formulas i.e. area is length x breadth, how to round off numbers.

Supporting the primary school child:

• Specific requirements from the school/teacher with regards to what method is used. May vary from school to school. What method works for you?
• Break multi-step problems (including equations with several computations, word problems, etc.) into smaller parts. Often each step counts 1 mark. Skip a step and you lose marks.
• Have a rule book and write them down for reference purposes.
• Encourage students to practice using a calculator.
• Use mnemonics to help students remember steps to Math algorithms. For example, Daddy, Mama, Sister, Brother can be used for the long division algorithm (Divide, Multiply, Subtract, Bring down).

For high school students:

Same ideas apply

#3 Understanding concepts:

A child:

• Has difficulty in understanding how numbers relate to each other, sequencing….
• Struggles to use number lines and the ability to create a visual image of number positions (before, after, between) …linked to using mental pictures to represent Math concepts,
• Struggles to understand and learn vocabulary…. zero. more than, less than, fewer than, place holder, divide, sum of, perimeter, …
• Has problems transferring concepts learned in the math classroom to real life situations like telling the time and being able to use money, graphs and measurement. Do they know the difference between g or kg, m or km, s or mins? (difficulty with decimals, rounding off)
• Not able to guestimate…how many marbles are in the jar? Can they estimate or do they want to try and count?

Supporting the primary school child:

• Use real objects to explain concepts i.e., pizza for ratio and fractions, then pictures and finally visualize the problem or sum.
• Guide students in visualizing patterns.

Supporting the high school child:

• Being able to visualize the problem, the shape, the pattern, etc.
• Draw it out or write it out using symbols.
• Use daily situations like using recipes, reading time tables, calendars, etc. % discount on sale items. Make the problem relevant to them…Math Literacy

#4 Math Problem-Solving

A child:

• Has difficulty reasoning through a problem, or difficulty using strategies effectively during problem solving.
• Has difficulty using mental pictures (such as patterns or shapes) to represent math concepts, or has difficulty “seeing” the math problem in his/her mind.
• Doesn’t know how to get started on word problems, or how to break problems down.
• Could be linked to poor reading-comprehension skills. Language processes could also create problems with the understanding of specific terminology, e.g., addition/plus/ altogether. Children often think that the word ‘calculate’ means that it is an addition sum…. link to number vocabulary in previous point.

Supporting the primary school child:

• Have real objects or draw pictures to represent what is going on in a word problem.
• Propose a number sentence, e.g., 6 + 4 and have them come up with a story problem for that number sentence.
• Keep the story the same, but make the numbers smaller, until they understand the problem being asked and then go back to using the original numbers.
• Provide students with a general strategy which can be used in many problem-solving situations, i.e. Who? What? Where? How?

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