- What your student is learning at school and;
- How the student is learning to do it.
I’m sure you heard many reasons why supporting the math curriculum and its teaching strategies at home is beneficial to the child - they are all true. But here is what I consider the main one: it supports your child’s confidence in mathematics. Higher confidence leads to better results in math. Simple as that.
If you simply jump into doing math the way you are used to doing it, you may not be supporting your child in the curriculum expectations and as a result they may not score well (even if they understood it). And that will shake their confidence in math. This confidence is crucial for your child’s math success.
The good news is that math has not changed.
There has not been some shattering breakthrough in math that discounts everything we know since you went to school. Math does not work that way. We build on it, sure, and find different ways of doing it, and progress forward with ideas and knowledge and discoveries, but rarely do we fully discard what we have learned so far.
So, parents, the math you have learned in school is still valid and it still exists.
But if that is true, then why so many parents have difficulty with it?
Because how math is taught did change. Just a little bit.
To be honest, probably the main area of confusion are the number sense units (addition, subtraction, multiplication, division) - and that is what this post mostly concentrates on. In another post I will also discuss Patterning and Algebra (starting around Junior Division years) which is a close second.
“base ten blocks”, “arrays”, “skip counting”, “counting up”, “making 10”, “place value”, “adding on”, “open arrays”, “splitting” and the list goes on.
If you simply jump into doing math the way you are used to doing it, you may not be supporting your child in the curriculum expectations and as a result they may not score well (even if they understood it). And that will shake their confidence in math. This confidence is crucial for your child’s math success.
The good news is that math has not changed.
There has not been some shattering breakthrough in math that discounts everything we know since you went to school. Math does not work that way. We build on it, sure, and find different ways of doing it, and progress forward with ideas and knowledge and discoveries, but rarely do we fully discard what we have learned so far.
So, parents, the math you have learned in school is still valid and it still exists.
But if that is true, then why so many parents have difficulty with it?
Because how math is taught did change. Just a little bit.
To be honest, probably the main area of confusion are the number sense units (addition, subtraction, multiplication, division) - and that is what this post mostly concentrates on. In another post I will also discuss Patterning and Algebra (starting around Junior Division years) which is a close second.
“base ten blocks”, “arrays”, “skip counting”, “counting up”, “making 10”, “place value”, “adding on”, “open arrays”, “splitting” and the list goes on.
Who can keep track of it all? Should you? What happened to the standard algorithms?
Here is the punch line: The standard algorithm is still used. In fact, the modelling tools and strategies mentioned above are the stepping stones to understanding the standard algorithm and efficiently perform mental math.
How we get to the standard algorithm and mental calculations is what changed.
The main reason for this change is to “help students gain a deeper understanding of mathematical concepts” (source: Number Sense and Numeration - Big Ideas). The idea is that students need to understand how numbers work, so that when they do get to the standard algorithm, they better understand why it actually works and be in a better position to evaluate if their answer ‘makes sense’. Likewise, it allows students to practice their mental math.
Think of the ‘new way’ of being taught as many different strategies. Students will naturally be drawn to one strategy over another and that is okay. The goal is to help students understand why they can manipulate numbers the way they do, not to make them use all strategies all the time.
I encourage you to make sure your student understands all strategies and the different ways of doing things. Many tests don't actually ask for one specific strategy or another, they just ask for “something” to be solved, and to show your work. Students can use whichever strategy works best for them and the problem they are trying to solve (within some guidelines). If they understand one strategy better over another, it is not tragic.
Example
Here is one example of a place value multiplication strategy.
Compute (158 x 7) using place value (hint: this is a strategy).
Here is the punch line: The standard algorithm is still used. In fact, the modelling tools and strategies mentioned above are the stepping stones to understanding the standard algorithm and efficiently perform mental math.
How we get to the standard algorithm and mental calculations is what changed.
The main reason for this change is to “help students gain a deeper understanding of mathematical concepts” (source: Number Sense and Numeration - Big Ideas). The idea is that students need to understand how numbers work, so that when they do get to the standard algorithm, they better understand why it actually works and be in a better position to evaluate if their answer ‘makes sense’. Likewise, it allows students to practice their mental math.
Think of the ‘new way’ of being taught as many different strategies. Students will naturally be drawn to one strategy over another and that is okay. The goal is to help students understand why they can manipulate numbers the way they do, not to make them use all strategies all the time.
I encourage you to make sure your student understands all strategies and the different ways of doing things. Many tests don't actually ask for one specific strategy or another, they just ask for “something” to be solved, and to show your work. Students can use whichever strategy works best for them and the problem they are trying to solve (within some guidelines). If they understand one strategy better over another, it is not tragic.
Example
Here is one example of a place value multiplication strategy.
Compute (158 x 7) using place value (hint: this is a strategy).
This is a code word for: decompose 158 into 100+50+8, then multiply each number by 7 and then add the partial products (students are taught patterns of multiplying by 10, 100, 1000 to be then able to solve the following decomposition):
100*7=700
50*7=350
8*7=-56
700+350+56 =(700+300) + 50+56=1000+106=1106 (This method separates the hundreds, tens, ones. Alternatively, at this stage, a standard algorithm can be used.) By the way, if you added in different order - that is okay!
No magic. Just new vocabulary. Isn't that how many of us implicitly compute in our heads anyways? So go ahead and support your students and how they are being taught math today.
To help you with that, my next two posts will explain some of the Primary and Junior division modelling tools and strategies used in addition and multiplication. (This ties back to my 2nd post – Strategies for helping your students in math at home - specifically - know the curriculum)
Looking Ahead to Intermediate and Senior divisions
Looking ahead to Intermediate and Senior divisions where the math problems are much more advanced, the models studied in Primary and Junior years will prove to be too cumbersome and more efficient strategies will be required in order to advance in the mathematical field, such as the traditional algorithms and efficient mental math.
Therefore, to prepare for that, I encourage your students in Primary and Junior division to practice regularly the following:
1. Math facts (addition & multiplication depending on division)
2. Mental Math Strategies (I suggest Singapore Mental Math workbook for this)
3. Word Problems workbooks. Emphasis on ‘show your work’ by utilizing the different models and math strategies (including word problem strategies such as understand the problem, make a plan, carry out the plan, look back OR think, solve, answer - whatever your school is using)
Exercises can be from school math book or the workbooks mentioned in the Links and Resources page. Singapore workbooks offer easy to follow mental math strategies and word problem exercises that are similar to the ones found in the curriculum, presented in a logical and concise order, making them ideal for at-home supplement.
Hope this helps!
Margaret
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