Margaret Math Help: 2015

Tuesday, December 15, 2015

In my previous posts I suggested that it is important to know both

What your student is learning at school and;
How the student is learning to do it.

Today I will talk a little bit about the How and why it is important.

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.

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).

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

Sunday, November 29, 2015

Links and Resources

Hello Everyone!

This page is meant to act as a resource for anyone who needs a starting point and it complements my November post on "Strategies for helping students in math at home". If you find another great resource and/or link please send me an email and I will add it to this page.

Ontario Curriculum

Here is a site dedicated for elementary teachers (K-6). It contains easy to follow e-workshops available for grades K-6. They are separated by divisions (Primary, Junior). They also talk about “Big Ideas” which is crucial to understand what the curriculum is concentrating on and where it is heading for each division - it it good to have a bird's view of where your child is moving towards!.

Below are just a few examples:

Primary (Grades K-3)
(Google it: “eworkshop grade 1ontario math curriculum”)

Junior (Grades 4-6)

A guide to effective instruction in mathematics - Kindergarten to grade 6

Intermediate (Grades 7-8) - Ontario Curriculum - Grades 1-8

University of Waterloo

Want to keep math fun and engaging? Look no further! University of Waterloo has a site developed just for that - for every grade (elementary and high school) and it complements the curriculum taught in school. It has content for both students and teachers, it has hundreds of fun web resources and games, including problem of the week and real life applications. Oh, and for the developer student you may have, it also has a site that introduces programming. As a bonus, it also has links to the famous University of Waterloo math contests for students of various grades.

It all happens at the Centre for Education in Mathematics & Computing.

Here are a few sub-links I picked out for you:

Various Other Interesting compiled links for online activities

For younger audiences (Kindergarten & Primary)

Useful Workbooks for your consideration

Here are some workbooks you may found useful. If there are others you have used please let me know and I will share!

1. Canadian Curriculum MathSmart or Complete MathSmart workbooks for the relevant grade (publisher: Popular Book Company).

http://www.popularbook.ca/our-products
Example (grade 1) : http://www.popularbook.ca/best-kids-workbooks-complete-mathsmart-g1.html?selectedId=93
Example (grade 1): http://www.popularbook.ca/best-kids-workbooks-canadian-curriculum-mathsmart-grade-109.html?selectedId=93

2. Complete Canadian Curriculum for the relevant grade – it provides curriculum based exercises for all the subjects, not just math (publisher: Popular Book Company).

3. Teacher Created Resources books (publisher: Teacher Created Resources) are great and fun activity books, especially for younger grades and/or summer fun.

https://www.teachercreated.com/books/math

4. Kumon Speed and Accuracy series – great in mastering addition &subtraction (more commontly known as math facts), multiplication, and division.

http://kumonbooks.com/books/by-series/speed-accuracy-workbooks/

5. Singapore Math (publisher: Singapore Asia publishers, Carson-Dellosa Publishing).

Example (grade 2): http://www.scholarschoice.ca/singapore-math-gr-2-429821.html
Example: http://www.carsondellosa.com/search-catalog/?q=singapore%20math

I have seen the above books in Scholar’s Choice, Mastermind Toys, Chapters/Indigo, Amazon, even Real Canadian Superstore and Costco at select times of the year (beginning of school and beginning of summer). I’m sure there are many others and all you have to do is Google to find these – these were just a few I have used in the past.

I do want to mention that while all these books are available online from most of the above mentioned places, I found Scholar’s Choice to be always stocked up with these books in-store, allowing a parent to browse through the content, look at specific examples, and then decide which book might be best suited for their student’s needs.

*Please note that I utilize 80/20 rule when publishing. Therefore, any errors that may arise in my blogs will be fixed as they are found.

Strategies for helping your students in math at home

You might be reading my blog and thinking that’s great that I need to address the gaps – but how exactly? And how do I know that my child has gaps?

In this post I will provide you with practical strategies to help your child at home, as well as some resources to supplement these strategies. If you feel you need me to address something even more specific, send me an email and I will do so!

1. Speak with the teacher

For Primary and Junior grades especially, an on-going communication with your child’s math teacher is very important. You will need to reach out and let the teacher know that you plan on being involved. At this point it would be helpful if you know what you are trying to achieve. I would suggest asking the teacher to let you know when a new unit is about to begin, and which one. Ask them to let you know right away if they notice that your child is falling behind on any concept, so that you can address that gap right away at home – do NOT wait until the test to find out (by that time the class would have moved onto another topic and most likely with other time pressures of other topics, you won’t address the gap adequately enough).

And you need to address it in a timely manner – because this unit will come back in the next grade for sure but in harder capacity, or in another unit if related.

Likewise, if you notice that your child is struggling with a concept but are unsure how to help them, let the teacher know and ask them to help them out/point them in the right direction.

For Junior, Intermediate, & Senior Divisions, ask your child to let you know when they are struggling – by that time they will be able to identify this. This will give you an opportunity to help your child right away. You will need to remind your child to speak to their teacher as required as well.

2. Know the curriculum

Do you know what is expected in each unit, at the grade level your child is at? Know what is in the curriculum and how it is being taught. Visit your provincial government website and dig in to review the curriculum.

Please take a look at the Links and Resources post I provided, for several helpful links. If you find a helpful link, please let me know and I will add it there!

3. Supplemental workbooks and Math Books

This option might be a little less daunting for some than the curriculum links above, and it is a great supplement for classroom teachings.

Consider getting a supplemental workbook resources (Canadian versions) and follow what they review in each unit. It is a great way to understand what is being taught in each unit and allows you to ‘learn’ with your child on what they are being taught at school. Many of these workbooks also walk through and ‘teach’ concepts with the student before doing the exercises. This will give you an idea not only what is being taught but how.

Ø Primary Division (K-Grade 3)

Working through workbooks is most likely sufficient at this stage.
You may want to consider online resources as well (like math games) to supplement the student’s learning as well as to keep it fun and engaging.
Please take a look at my Links and Resources post for several useful workbooks and online resources.
Library: I have seen many of the suggested workbooks in the local library as well. You can check these out and have your child complete the exercises on a separate piece of paper.

Ø Junior Division (Grade 4-6)

Same points as in the primary division above plus
Find out what math textbook(s) are used. Speak to your child’s teacher and ask that your child brings a book home either on the weekends or whenever they have a knowledge gap to address.
When a book makes it home, review how the concepts are being taught in the text book – although the concept is the same, it may be taught differently from the time you were in school. And it is important to support and supplement school teachings in the same manner (I have more to say on this topic in future posts).
If you can, I would suggest purchasing the school textbook for home use. Amazon.ca is a great place to find a used text book – just make sure you get the right version – ensure the ISBN number on the book you order matches the one used in the classroom.

Ø Intermediate and Senior Divisions

Ensure your child brings home their textbook and that they communicate with you and ask you for help whenever there is something they do not understand at school – and help them with it.
Check out the Links and Resources section of this blog for online resources.

A note about formal tutoring

There might be times when formal tutoring is required. This could be because you are not strong in math, especially in older grades, or that your child reacts better to someone else teaching them. In these cases, a formal tutoring is warranted. Just make sure the tutor themselves is well versed in today’s curriculum and they can communicate effectively with your child so the time is well spent.

A note about Singapore Math

If you feel comfortable with mathematics, I would strongly encourage you to look into Singapore math.

In the primary years, it very gracefully introduces 'number sense' mathematical topics such as addition especially with re-grouping (carry-over and borrowing) including the concept of converting 1 ten into 10 ones as required etc. It is easy to grasp and I personally believe a very good complement to the curriculum. It will make their understanding deeper and open their minds to the fact that there are more than one way of doing the same thing, and getting the same result. A concept that is well worth having early on in math to encourage thinking outside the box.

In junior years it very clearly teaches mental math strategies and problem solving strategies. Both concepts which I found not very clearly defined in the curriculum today. They are sprinkled all over the current curriculum with not enough time committed to them to fully master the concept. So practicing it at home is well worth it.

I have not explored the Intermediate and Senior level Singapore math books but as soon as I will I will let you know what I think!

4. Practice

It is important to practice. Why not get into a routine early in their school years to do homework or practice. It is much easier to establish that routine in primary and junior grades and then maintain in seniors years and reap the academic benefits that come along with it!

You pick which activity makes most sense for your situation and when – the suggestions below are meant to provide you with some ideas and are not an exhaustive list. These activities do not need to be long. Keep in mind that some school boards adapt a policy of 10 minutes per grade (elementary). Doing 1 page in the workbook may not seem like a lot and it will add up over time to bring in great results.

Don’t forget to keep it fun and engaging for students, perhaps mixing it up with online activities and real-life applications will keep them more interested (check out University of Waterloo link I provided in the Links and Resources post for real life example and engaging games!)

Some ideas are:

Complete any homework that came from school and address any gaps. This includes all homework, of course, not just math.
If math gaps exist, work with your child on addressing these gaps, either through you tutoring them and/or having them practice in their workbook.
If no homework and no math gaps exist, why not review the next concept in the unit, to allow your child a head start.
In Primary and Junior years, why not practice math facts as well as multiplication tables? Btw, that is a great summer activity (more to come on things to do in the summer).
Reinforce existing knowledge through an online activity.
Have fun doing these! Take it easy and enjoy what you are learning with your child. If they are having a particular hard time with a topic, take a break and pick up again next time or switch to an activity your child learns better from (maybe online). Do not make these activities a negative experience.
Acknowledge your child’s efforts – not all children will be at the same level, but they should all feel confident in doing math.

Happy Learning!

Wednesday, November 18, 2015

Addressing Gaps in Math knowledge

As a tutor, I often had students come to me and tell me they needed help to study for this next test (coming up very shortly) because their mark was low in math. As I work with the student I work through the material slowly and I ensure to stop on concepts that a student does not understand, ensure they understand it, and then progress to the next level with the ultimate goal to get them ready for the test. It is very possible that a student understands the topic but needs some extra help on specific item in that unit. We cover the concepts and topics, ensure understanding, and the student is good to write the test in confidence.

But what happens when the student does not understand the current topic because they don’t understand the previous related topic, and in some cases the previous one to that and so on?

That is exactly how students become discouraged in math. It’s because they went down a path without full understanding of a concept/topic and now they are so far down they are lost in the unknown. This is where a good teacher shines. You see, you must keep on going ‘back’ in concepts that are related, until you find the root cause (the beginning of) the students’ confusion.

And you begin there.

Test or no test looming, you must start from that point or you don’t stand a chance in helping this student understand this particular math concept, and in some cases, math in general.

Allow me to give you a practical example. A grade 9 student doing a geometry unit – specifically on congruent triangles. They may need to prove that two triangles are congruent. But these triangles are embedded inside other triangles and/or a parallelogram with additional information provided. For this exercise they will need to do some deductive work. Meaning, figure out what they do know and how to find the rest of the unknowns to ultimately get them to prove the triangles are congruent.

They may need to know some theorems (e.g. Pythagorean), rules such that all angles always add up to 180 degrees in a triangle, definitions, or trigonometric functions, depending on the nature and complexity of the question.

It is one thing to help a student ‘deduce’ the answer when they understand how it was deduced. In that case the student can practice their deduction skills. But what if a student did not understand the deduction steps? Then you need to backtrack their knowledge line and see where the breakage happened. Do you need to review the geometric rules? Do you need to review the trigonometric functions concepts? If yes, do you need to go back all the way to definitions of adjacent side, hypotenuse, opposite sides of a triangle? Do we need to review the SAS, SSS, ASA congruence rules? Figure out how far back to we need to go …and go there.

On a simpler level, how about a child learning how to add double digits and re-grouping? If they don’t understand – do you continue or do you pause and try to figure out what it is they don’t understand? In this case you might need to go back and review single digits. You might need to review the concept of ones and tens and what does it mean and do some related exercises. You may need to break the number up into ones and tens and manipulate the numbers slightly differently if a child understands it a certain way. In other words, go back as far as necessary and stay there as long as necessary until the concept is well grasped. Then move forward. This may require a few sessions depending on how far back you had to go and the age of the student.

The effort is well worth it.

Because once you fill in the knowledge gaps for the student, suddenly everything makes sense. Math makes sense. Confidence returns and math results improve.

You may find me sprinkling this topic throughout my blogs going forward, as I truly believe this being the number one reason why kids fall behind in math – they develop knowledge gaps that are not resolved.

My next blog will discuss preventative measures to ensure any knowledge gaps are addressed in timely manner.

Friday, September 25, 2015

Welcome & Introductions

Welcome to my blog! As my Vision and Mission state, this blog is dedicated to mathematics and trying to help as many parents out there as possible to help their children in math. I hope to share my knowledge with you all and welcome any feedback or questions or topics you would like me to address through this blog. Please feel free to email me anytime. It goes without saying that this blog is my opinion only and I respect that some may have different views.

A little bit about me:

I graduated from University of Waterloo, Bachelor of Mathematics, Combinatorics & Optimization Major. And I loved it. The world of possibilities and applications that exist in mathematics is limitless and solving problems logically and mathematically is fascinating and…fun. I am however, able to say this only because I understand math. I get it. And what’s more, I know how to explain the concepts to someone else so that they understand it too.

And I'd like to think I’ve had plenty of practice…with good results. Beginning in Grade 9 and all through high school I signed up for a peer tutoring program, where I would help fellow students who were struggling with mathematics achieve their goals. And they did. In grade 12 I signed up for a teaching assistant program where I helped a teacher in grade 9 math course and the students in it. After graduation I went on to tutor high school students who were children of my friends.

I tutored one student who came to me in the 2^nd half of the semester, failing with a 47%. Their final mark was 63%. And that’s only because we had limited time to learn before semester ended – I’m sure it would have been higher still should we had more time. They started enjoying math and doing the exercises; they gained confidence in their ability to understand math.

Every student has the ability to succeed in math.

Through my tutoring years and on-going math teaching to children the same common themes pop up, that once addressed, help them overcome their math fears and misunderstandings:

Often gaps in math knowledge, when found and addressed, accelerate student learning drastically and increase confidence and likeness of the subject. So go look for them!
There is always more than one way of explaining the subject/problem (and the solution) – effective teachers* accept different ways of getting to the solution and nurture that thought process. There might not be one way fits all thought process.
Memory work, especially in younger grades such as times tables, additions, subtractions, formulas, etc., is a necessary base for progression in mathematics. Math exploration is not enough to advance and progress in mathematics to the more difficult stages. I am fully aware there might be some who would strongly disagree but I truly believe that one must not only grasp the basics but have them at their fingertips to advance in the subject.

In this blog I will explore these points further, suggest ways of giving students a head start on mathematics and how doing a little bit each day can have dramatic results in the future, as well as discuss how to help your children at home and complement school taught topics.

Before I close off, I would like to share with you that I did not always understand math, in fact, I hated it in grade 4... and now I have a Bachelor's of Mathematics. I hope to help you help your students who may be struggling in this subject as well, perhaps giving up on math, and helping them understand it in hope that a a light will come on and math will once again make sense.

This blog is about empowering you to help your children/students succeed in math. I look forward to helping everyone who needs help in math.

Thank you for reading!

Margaret

* By ‘teacher’ I mean anyone who is helping and/or tutoring a student in mathematics. This can be a certified teacher, a parent, a friend, a tutor, grandparent…you get the idea.

Margaret Math Help