Supporting your child in learning math Marian Small November 2017

This morning I will talk about How the teaching of math has and has not changed Things you can do to support your child’s math learning

What math skills are important in 2017 and beyond? The world has changed. In the past, much of early math learning focused on how to efficiently add, subtract, multiply and divide. But often students did not learn, well enough, when each operation is required.

For example, if the problem were: How many boards that are 4 For example, if the problem were: How many boards that are 4.2m long do I need to fill a 17.59 m space?, a students needs to know whether to add, subtract, multiply or divide.

Although I want students to be able to compute, being quick at it with large numbers matters less when we all have calculators available. Knowing when to use each needs more of our teaching time.

Problem solving There is also a need, in the society in which we live, to create more students who are good problem solvers- people who can figure things out without being shown first. Employers regard this as a HUGE need.

Historically Many students, even those who were good at computation, fell down at problem solving.. So now it gets more emphasis.

There are 5 strands in K – 6 math in the Ontario curriculum Number Geometry Measurement Patterns and algebra Data and Probability

Most parents are most concerned about number, so I will start there.

Working with numbers The way we approach the learning of computation has changed in some ways, but not other ways.

Little number work Facts involve computations with small numbers, e.g. 4 + 9 = 13 or 12 – 3 = 9 or 9 x 8 = 72 or 40 ÷ 5 = 8. Facts remain important because they are fundamental both to estimation and any other calculations.

We used to believe… The best way to learn facts is to sit down and memorize them by saying them over and over. And that being super fast with them is really important.

Now we realize… that a child is better off if he or she has tools to recall something he or she may have memorized but may forget. We call these strategies.

For example… Whenever you add something to 9, we focus on the notion that you could, instead, add the number that is 1 less to 10. e.g. 9 + 8 = 10 + 7 Later 299 + 215 = 300 + 214.

There is now research that shows… That even though some kids memorize well.. for kids who are anxious about math or get nervous having to be quick, old strategies doom them to failure.

There is now research that shows… Brain research shows that when a student is anxious, it is very hard for him or her to recall facts, even if they know them(Sian Bellock) We now approach fact learning in different ways for different kids.

So we teach principles and strategies For example, we spend time with kids helping them know (just like you and I did) that 14 = 10 + 4, that 18 = 10 + 8, etc. There is no work to adding 10 + 4; it’s just what 14 is.

Then We spend LOTS of time getting kids good at adding numbers that add to 10 and then use those to figure out other questions. For example 8 + 5 is 8 + 2 and then another 3, but 10 + 3 is 13.

So we teach principles and strategies For some reason, people learn doubles quickly, so to figure out 7 + 8, we help kids think: 7 + 7 and then 1 more.

For multiplication We help kids see that to figure out 4 x 7, you could really think 4 x 5 + 4 x 2. o o o o o x x

Many of these principles can be.. Seen on addition and multiplication tables visualized using diagrams or objects

We use new tools We now use many visual/concrete materials so students can “see” the math ideas. A long body of research has shown their value in making math make sense to kids and in improving performance.

Accessing virtual manipulatives There are tools for materials your children use in class freely available on line. Many are also available as apps.

Math tools 10-frames It’s easy to see why 9 + 9 = 10 + 8 (18). Just move one counter up.

Pattern Blocks http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/ubPatternBlocksToolCreator.swf

Pattern Blocks http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/ubPatternBlocksToolCreator.swf

Pattern Blocks APP: Pattern shapes

Rekenrek http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/Rekenrek1.swf

App Number Rack

Hundreds chart http://nlvm.usu.edu/en/nav/category_g_2_t_1.html

App Interactive Hundred chart

Base ten blocks https://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/gr3-5/itools_intermediate_9780547274058_/basetenblocks.html

Base ten blocks

App Base ten blocks math

Relational rods http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/ubRelationalRodsCreator.swf

App Number rods

Fraction bars http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/FractionStrips1.swf&title=Fraction%20Strips

Or

Geometric shapes http://illuminations.nctm.org/Activity.aspx?id=3521

Attention to estimation There is increasingly more focus on estimation and mental strategies, when appropriate, when dealing with larger numbers (e.g. 3- digit, 4 –digit) and decimals.

Estimation I need kids who quickly see that 35 x 49 must be around 1500, not just kids who get the answer; often an estimate is all this is needed to see if your calculator answer makes sense.

For mental strategies Here is an interesting mental strategy we often teach younger kids for adding and subtracting.

Use a 100 chart 44 + 32

Use a 100 chart 44 + 32

Subtracting on a 100 chart 65 - 19

Subtracting on a 100 chart 65 - 19

Alternative strategies that might seem new How would you calculate 342 – 121? Would you do 200 – 2 the same way? Children are learning different strategies since different ones are more efficient or more meaningful in different situations AND Different ones make more sense to different kids.

For example It is reasonable and correct to add like this: 38 + 47 70 + 15 85

For example It is reasonable and correct to add like this: 38 + 47: Think 38 + 50 = 88 and then subtract 3 to get 85.

Or subtract like this... 100 = 99 + 1 - 79 - 79 20 + 1 = 21

Teaching through problem solving We show kids we have faith that they can figure things out. What happens is that as they solve a problem, they clarify a lot of ideas.

I might ask… I bought 5 items and spent $315. Two were the same price. One cost a lot more than the others. What could each have cost? Could be 10 or 20 for bill

I might ask The volume of a box is 100 cm3. What could the length, width, and height be?

Collaboration Kids will be working together more to learn since most of us learn better in talking with others.

Do they all have to do exactly the same thing? We might offer two or more tasks for students to choose from. The tasks will be similar in nature, although one might be slightly less complicated than the other. This serves different needs better than we used to in the past.

What can you do? Our big question as parents is what we can do to help our child.

Number Play Lots of children respond well to “magic”. For example: I subtract 4 from what they say

Number Play Choose a number. Add it to itself. Add 5 Add 6. Subtract 1 Divide by 2 Tell me your answer and I will tell you your number. Subtract 5

How many….? Spoons in the drawer? Steps to get downstairs? Trees on the street? Sections in an orange? Windows in the house? 11 sections in an orange

Interesting Questions How long is long hair? How long would it take to count to 100? How far could you go in 100 steps?

Support involves… Not showing, but probing. Asking why this or why that… Building connections

You might Encourage kids to “teach you” what they learned or explain their thinking to you.

Games You could play games where you make up the rules or use existing games to practise skills.

Games to Play 2 players Each rolls two dice. The score is the sum. The first player to get to 100 wins.

Games to Play 2 players Each rolls two dice. The score is 2 x one value + the other. The first player to get to 100 wins.

Board games

Box cars and one eyed jacks http://www.boxcarsandoneeyedjacks.com/

You could solve interesting problems

How much is your name worth? B C D E F G H I 1 2 3 4 5 6 7 8 9 J K L M N O P Q R 10 11 12 13 14 15 16 17 18 S T U V W X Y Z 19 20 21 22 23 24 25 26

What words are worth 40 – 50? S T U V W X Y Z A B C D E F G H I J K L 1 2 3 4 5 6 7 8 9 J K L M N O P Q R 10 11 12 13 14 15 16 17 18 S T U V W X Y Z 19 20 21 22 23 24 25 26

Figure this http://www.figurethis.org

Figure this

Useful web sites http://www.dreambox.com/parent-resources http://www.cbc.ca/news/health/back-to-school-2015-parents-math-anxiety-can-pass-to-kids-psychologists-say-1.3207956

Useful web sites https://www.edu.gov.on.ca/eng/literacynumeracy/parentGuideNumEn.pdf • http://www.ocdsb.ca/med/pub/OCDSB_Publications/Numeracy%20Parent%20Guide.pdf

What is success? Not just a mark Enjoying the math Seeing math around them

You need to… Show that you enjoy math too. Show confidence- believe that they can if you give them the time. Emphasize good thinking, not speed. Emphasize good thinking, not mistakes.