Math Tutor, Edmonton

Reminder that I will be at the North Vancouver City library from 11AM-1PM for the drop-in tutoring session. Come by if you need some help with your studies!

Week of September 24

Topic of the week: fractions as they relate to the acquisition of higher level math skills

1. I’m going to break this week’s topic down into two parts:
a) why a solid foundational understanding of fractions is important
b) my thoughts on why so many students struggle to develop this understanding

Firstly, why is an understanding of fractions so foundational to developing higher level math skills? The introduction of fractions in a student’s mathematical education signifies their initial exposure to ratios. And as their education continues over the course of their academic career, understanding and analyzing ratios is necessary in virtually every other math concept that a student will encounter (geometry, algebra, trigonometry, calculus), not to mention every aspect of the sciences (biology, chemistry and physics). A limited understanding of fractions (ratios) in early math education can lead to much more difficulty in grasping major concepts as a student’s education progresses, and may compromise their learning in all of these areas.

Next, why do so many students struggle with fractions? The first place to start would be to define what “fraction” actually means. In the most basic way, a fraction represents a part of something, or a portion of something that is whole. In essence, it is a representation of division, and in my experience, division is the basic mathematical operation that students struggle with the most. Couple that with the fact that many students have not yet mastered multiplication and division facts, or the ability to recall them with ease, and working with fractions becomes increasingly difficult. It has also been suggested in the research that many teachers do not have an in-depth conceptual and procedural understanding of fractions themselves, making it problematic to convey a deep understanding to their students. Of course, there are a multitude of things going on, but in my opinion, these are two of the major roadblocks that get in the way for many students.

A componential view of children's difficulties in learning fractions Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articula...

Week of September 24

Topic of the week: fractions as they relate to the acquisition of higher level math skills.

3. Resources
I really like the Math Antics guy for instruction on a multitude of different math concepts, and I use his videos and practice sheets a lot in my classes. The kids sometimes tell me that he’s kind of “cringe-y” but they are always silent and watching as soon as I turn the videos on. I would encourage you to check him out if your kids are struggling with a particular concept. Here is a video of him talking, in a very basic way, about fractions:

Math Antics | Basic Math Videos and Worksheets This website requires cookies to be enabled in order to work properly. But don't worry, we do not use third-party cookies or track your activity on other sites.

Week of September 24

Topic of the week: fractions as they relate to the acquisition of higher level math skills.

2. Mythbuster
Myth: Some people are just inherently good at math.
Busted: While there is some evidence to suggest that there may be a “genetic” component to the acquisition of math skills, this would only apply to a very small fraction of students. See what I did there? Learning math is no different than learning any other skill. The more you do it, the harder you work at it, and the more you commit to improving at it, the better you get.

Week of September 24

Topic of the week: fractions as they relate to the acquisition of higher level math skills.

1. I’m going to break this week’s topic down into two parts:
a) why a solid foundational understanding of fractions is important
b) my thoughts on why so many students struggle to develop this understanding

Firstly, why is an understanding of fractions so foundational to developing higher level math skills? The introduction of fractions in a student’s mathematical education signifies their initial exposure to ratios. And as their education continues over the course of their academic career, understanding and analyzing ratios is necessary in virtually every other math concept that a student will encounter (geometry, algebra, trigonometry, calculus), not to mention every aspect of the sciences (biology, chemistry and physics). A limited understanding of fractions (ratios) in early math education can lead to much more difficulty in grasping major concepts as a student’s education progresses, and may compromise their learning in all of these areas.

https://demmelearning.com/blog/fractions-higher-math/

Next, why do so many students struggle with fractions? The first place to start would be to define what “fraction” actually means. In the most basic way, a fraction represents a part of something, or a portion of something that is whole. In essence, it is a representation of division, and in my experience, division is the basic mathematical operation that students struggle with the most. Couple that with the fact that many students have not yet mastered multiplication and division facts, or the ability to recall them with ease, and working with fractions becomes increasingly difficult. It has also been suggested in the research that many teachers do not have an in-depth conceptual and procedural understanding of fractions themselves, making it problematic to convey a deep understanding to their students. Of course, there are a multitude of things going on, but in my opinion, these are two of the major roadblocks that get in the way for many students.

https://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/

Fractions Are Critical for Success in Higher Math What is it about learning fractions that is so powerful? This blog post will answer that question and show you why you need to make sure your student really masters fractions.

Reminder that tomorrow (Saturday) is the free drop-in Math tutoring session from 11am-1pm. I’ll be at the West Vancouver memorial library, so if anyone is needing help with homework, studying for a test or clarification on a math concept, stop by and we can work on it.

Week of September 18

Topic of the week: rote memorization of multiplication tables and division facts

3. Resources

For multiplication tables (and division facts), the quickest and easiest way to build capacity is by using worksheets and blank multiplication tables (flash cards can be added to the mix as well), and then practice, practice, practice. Everyday. Now this is simply to help your kids develop an ease of recall of these facts, so that they do not use precious working memory when dealing with more complex problems, and can easily retrieve this information from long term memory. It does not, on its own however, lead to a deeper understanding of those concepts. This is achieved with higher level practice.

Week of September 18

Topic of the week: rote memorization of multiplication tables and division facts

2. Mythbuster
Myth: rote learning is bad.
Busted: “In her book, Seven Myths About Education, teacher and educationalist Daisy Christodoulou argues that memorizing doesn’t prevent understanding but rather is vital to it.

“Saying all these negative things about rote learning [versus understanding] is very unhelpful,” she says. “The two things are not in opposition. It’s not that we should spend time on conceptual understanding instead of spending it on learning times tables. It’s by spending time on times tables that you’ll develop the conceptual understanding. Having times tables, basic math facts, phonics, spelling and grammatical structures really well established will allow you to speed up later on.”

https://www.edubloxtutor.com/rote-learning/ #:~:text=Memorization%20vital%20to%20understanding,very%20unhelpful%2C%E2%80%9D%20she%20says.

Week of September 18

Topic of the week: rote memorization of multiplication tables and division facts.

1. There has been a significant push against the use of rote memorization as a tool in learning and education over the last few decades. While I am a huge proponent of critical thinking, contextual learning and the importance of having a deep understanding of concepts to support the learning and assimilation of new material, I believe that it is a mistake to discount the importance of rote memorization in certain contexts.

In particular, I believe that memorization is crucial when it comes to learning and recalling multiplication and division facts. While I believe that all students should have a solid understanding of the foundations of multiplication and division, I also believe that rote memorization of the basic facts, as early and as quickly as possible to promote ease of recall, will provide students with more capacity to develop those deeper understandings. The caveat here is that your kids will need to have a good understanding and recall of addition and subtraction facts, since multiplication is just repeated addition and division is just repeated subtraction.

See the following article for perspective on this:
https://www.herts.ac.uk/link/volume-2,-issue-1/is-there-a-place-for-rote-learning-multiplication-tables-in-english-primary-schools #:~:text='Rote%20learning'%20is%20the%20method,they%20can%20be%20recalled%20accurately.

TOPIC: what to expect from this page

This page is meant to augment my tutoring sessions, as well as provide parents/guardians/supporting adults with additional tools to help their kids experience enjoyment and success with their math studies.

Each week, I will endeavor to post the following:
1. The topic of the week and some background about it.
2. Mythbuster: I will bust a math myth.
3. Provide evidence-based research on the topic of the week.
4. A video lesson or resource.

I will also post daily practice questions, and throw in some fun math riddles and brainteasers too.

I hope you will find this page and its resources useful on your math journey.

TOPIC: supporting your kids with the basics

In my experience as a math teacher and tutor, I have found that the most common gap for young people as they progress with their math studies is the lack of a robust understanding of fractions. And in tandem with this, difficulty recalling multiplication and division tables/facts.

The good news is that it is never too late for your kids to learn these basics. Once they do, they will be able to grasp more complex operations and concepts in a fraction of the time. See what I did there?

Over the next several posts, I will provide resources, links and instruction on how you can support your kids in the mastery of basic multiplication and division facts, and a series on understanding, working with, and manipulating fractions.

I am currently accepting students for the 2023-2024 school year, grades 4-12, and have single student sessions as well as group sessions available.

Rates:
Single student session: $40/hour
2-student session: $50/hour ($25 per student)
3-student session: $60/hour ($20 per student)