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Students Struggle with Math - Especially in Saskatchewan - What Can We Do To Help Them?

Saskatchewan grade 10 students’ scores had an average of 468 points, while the average Canadian grade 10 student scored 497. This means that Saskatchewan grade 10 students were approximately two years behind average in math compared to students in the rest of the country in 2022!

Math is difficult for many students.

The subject students tend to struggle with the most is math. Why is this? Of course, COVID-19 and its disruption on schools and learning did not help matters, but even before COVID-19 the subject students tended to struggle with the most was math.

While I was fortunate to always be good in math and find it easy (scoring the second highest mark in Saskatchewan in a math competition in grade 6 and always at the top in my school), I know that for other students it is not as easy.

A few of my classmates in Educational Math classes (students who were also becoming high school math teachers) wanted to become math teachers because they had struggled in math and they wanted to help students who struggled like they did. I wondered how they would pass the university-level math classes that we needed to take to earn a Bachelor of Education degree with a major in Mathematics Education. They managed, they might not have earned the top marks, but they managed.

Even students who are good at math seem to fear some levels of math. It is well-known that Mathematics Education majors at the University of Regina must take one 300-level math class. Not a big deal, right? These are students who want to become math teachers, they are probably good at math and love math. Not exactly! To my knowledge, I am the only Mathematics Education major who graduated in 2004 who took an “actual” math class as their 300-level math course (Linear Algebra III), rather than a course about the history of mathematics.

Therefore, I set out on a quest to discover statistics (statistics is my favourite area of mathematics!) about students struggling with math and the reasons for which many students struggle with math, as well as how we and others can help.

How Serious is the Problem? How Much Do Students Struggle with Math?

  • In 2022, it was found that grade 10 students in Saskatchewan were tied for last place with grade 10 students in New Brunswick, with an average score for math on the PISA (Programme for International Student Assessment) of 468. This was a drop of 17 points from 2018 scores, which is significant as PISA equates a 15-point drop to the elimination of a year of learning. Therefore, on average, Saskatchewan grade 10 students, in 2022, knew a little more than a year of learning less of math than Saskatchewan grade 10 students did four years earlier. Saskatchewan grade 10 students’ scores had an average of 468 points, while the average Canadian grade 10 student scored 497. This means that Saskatchewan grade 10 students were approximately two years behind average in math compared to students in the rest of the country in 2022! Quebec had the highest average at 514. (Source: https://www.oecd.org/en/publications/pisa-2022-results-volume-i-and-ii-country-notes_ed6fbcc5-en/canada_901942bb-en.html)

  • In a global context, Canada scores well, behind only eight other areas in the math category (Singapore, Macao (China), Chinese Taipei, Hong Kong (China), Japan, Korea, Estonia, and Switzerland). However, math scores have steadily declined across all Canadian provinces since 2003 and one in five Canadian students performed at the lowest level on the PISA, below Level 2. Only 12% of Canadian students ranked as high achievers, scoring at Level 5 or Level 6 (in Singapore, 41% of students scored at the top level). (Source: https://tnc.news/2023/12/05/students-math-scores-drop/)

  • Even back in 2003, Saskatchewan students performed significantly below the Canadian average in all four areas of mathematics that were tested on the PISA (space and shape, change and relationships, quantity, and uncertainty) and Saskatchewan was the only non-Maritime province to score significantly below the Canadian average in any of the areas. (Source: https://www.cmec.ca/docs/pisa2003/pisa2003.en.pdf) This is particularly interesting because, since 1993, Saskatchewan has been part of the Western Canadian Protocol (now renamed as the Western Northern Canadian Protocol) for Collaboration in Basic Education Kindergarten to Grade 12 for mathematics, along with Alberta, British Columbia, Manitoba, Northwest Territories, Yukon Territory, and Nunavut. Therefore, we have the same curriculum as they use in Alberta, and Alberta students performed significantly above the Canadian average in all four areas of mathematics, and in British Columbia, the students performed significantly above the Canadian average in uncertainty. No other province that uses the Western Northern Canadian Protocol performed significantly lower than the Canadian average in any of the four areas of math. What is particularly sad, in my point of view, is that Saskatchewan students performed the same as the Canadian average in terms of interest and enjoyment in mathematics, belief in the usefulness of mathematics, perceived ability in mathematics, and mathematics anxiety. However, Saskatchewan students performed significantly lower than the Canadian average in terms of mathematics confidence. The Saskatchewan students are not less disengaged in math than the average Canadian student, they want to learn! Therefore, this is an indication that it is the schools that are failing them - not the curriculum, and not their levels of engagement in mathematics.

  • In 2022, the average fourth-grade mathematics score on NAEP (National Assessment of Educational Progress) mathematics scales in the United States decreased by 5 points and was lower than all previous assessment years going back to 2005. Meanwhile, there was an overall decline in eighth-grade mathematics scores for the first time since the initial mathematics assessment in 1990. (Source: https://nces.ed.gov/fastfacts/display.asp?id=514)

Why Do So Many Students Struggle with Math?

Abstract Concepts

As math teachers, we learn about the concrete-to-abstract continuum. If you ever wondered why you started with blocks in math class, then had pictures, and then had numbers for some skills - this is why! Many students find math difficult because it is hard to visualize math or relate it to everyday experiences. That is why we, at Clever Minds Online Learning Centre, use as many examples related to the real world as possible when teaching math.

Missed a Step? That Makes Life Very Difficult in Math!

Math builds on itself, with each new concept depending on the understanding of previous concepts. If a student misses or does not fully grasp a concept, all the later concepts that rely on understanding that concept become much more difficult to master. It is like they are a brick wall and as the wall is being built there are an increasing number of missing bricks in each higher row. This is why we provide Math Assessments, find the weak or missing areas in the student’s math history, and work with them and their family to build a sturdy foundation! Here are some middle years math resources that can help with practice and review.

Tip for Parents: Quiz your kids on their basic math facts from a young age, make a point to especially meet with their math teacher and ask the teacher what your child’s weak areas are in math, then work on those skills with your child - or have us help your child with those skills!

Problem-Solving Skills

Students often ask, “When am I ever going to use this in real life?” in math class. Even as a math teacher, I will be honest and say that there are some concepts in high-level math classes that you will likely never use in real life unless you are a high school math teacher in real life! However, math teaches students how to think, solve problems, and use logic!

The problem is, we start teaching math to students who are four years of age, but the rational part of the human brain is not fully developed until people reach approximately the age of 25!

Does this mean that we should not teach math to people until they are 25 years of age? No! Absolutely not! We are talking about when the rational part of the human brain is fully developed, it starts developing much earlier than that. In fact, the brain of a five-year-old child is approximately 90% the size of that of a fully grown adult. The early years are the best opportunity for a child’s brain to develop the connections that are necessary for them to become healthy, capable, successful adults. The connections needed for problem-solving are formed in the early years - or not formed. It is critical that the connections be formed in the early years because it is much more difficult for these brain connections to be formed later in life. Between ages 4 and 7, the child develops primitive reasoning. Inductive reasoning is developed between ages 7 and 9. Between ages 11 and 14, the youth solves more complex problems and develops abstract thinking and deductive reasoning.

Since their brains are just starting to learn how to solve problems, having concrete steps for solving math word problems can be very helpful. That is why we teach how to solve math word problems in a very step-wise manner. They need to be taught how to approach a problem, choose the correct method, apply it correctly, and check that their answer is correct (or at least reasonable).

Tip for Parents: Ask your kids to help you solve math puzzles in everyday life - like, if you are shopping and a shirt is 20% off, ask them how much it will cost. If you are baking and tripling the recipe, ask them how much of each ingredient will need to be used.

Anxiety

Students know that math is one of the most important subjects, which explains why it is even more stressful for them when they have trouble with the subject area. This anxiety can interfere with a student’s ability to focus and think clearly. This is why we help students by providing them with practice tests, support, and study skills.

Tip for Parents: Do not admonish your child when they get a bad grade on a test. Rather, discuss grades on tests openly and honestly from a young age. Ask them what marks they get, whether they are happy with those marks, how much they study before the tests, how they think they could improve their performance on tests, etc. Be sure to feed them a healthy and nutritious breakfast every day, especially on days when they have tests!

Teaching Methods

How math is taught can also impact how well students understand it. While I was good at math, that does not mean I always had a deeper understanding of the topic. For example, I knew that the process to find the x-intercept was to set y equal to zero and solve for x and that the process to find the y-intercept was to set x equal to zero and solve for y. I did not know why that was the process, I just knew it was the process. I had a lightbulb moment in university when I realized why that was the process, it was so obvious, but no teacher had ever told me why that was the process! That is why we do not simply tell students the steps to solve problems in math, we explain why the steps are taken to solve problems! We want students to understand math on a deeper level, we want them to have a very strong foundation to build on!

Tip for Parents: At the supper table, ask your kids what they learned in math class that day. Ask them to explain how to answer questions of that type, ask them to explain math concepts, etc. Maybe this will help you relearn some math skills that you forgot about a long time ago!

Lack of Practice

Have you gotten good at a sport, playing a musical instrument, or beating others at a board game? How did you get so good at it? We bet that it was practice! In his bestselling book, Outliers, Malcolm Gladwell repeatedly refers to the “10 000 hour rule,” asserting that the key to achieving true expertise in any skill is practicing in the correct way, for at least 10 000 hours. Do you think your kids have done 10 000 hours of math during their lifetimes?

This is why we talk to parents and students about spending enough time each week on schoolwork. In general, students should spend 10 minutes x their grade level on schoolwork 5 times per week. For example, if a student is in grade 5, they should spend 10 minutes x 5 = 50 minutes, so 50 minutes on schoolwork five times per week. Generally, we recommend they do schoolwork on Monday, Tuesday, Wednesday, and Thursday, and then it is their choice of when they do schoolwork on the weekend.

When students are in high school and struggle in math, we recommend they spend at least five hours per week outside of school on math. We know that they might have a test in other subjects coming up, or they might need to write an essay, so these five hours can be placed flexibly throughout the five sessions. Of course, our weekly sessions with students count towards these five hours, so if a student gets help with math from us for two one-hour periods per week, they only need to do three hours per week of math on their own. This also helps to ensure that their math is being completed correctly.

Tip for Parents: Make sure your kids are using day planners, whether they are paper or electronic, and help them schedule the five blocks of time for schoolwork each week. Ask them what homework they have, and whether they are behind on anything in school (help them to make a plan to catch up if they are). Talk about when, during the day/evening, they are the most energetic and how they can best use that time to focus on schoolwork (and which subjects they should work on during those time periods).

Fixed Mindset Rather than Growth Mindset

Some students might think that they will always be bad at math, maybe a teacher even told them at one point that they are bad at math! We support, encourage, and uplift our students and fill in their previous gaps so they know they are prepared to do well in math! If students stay stuck in this mindset, it can hinder their willingness to work on math and to persevere when they struggle with math. Additionally, having someone to help them with their math makes the challenges much easier! Many students do not like the feeling of their brain becoming tired from thinking hard. However, with practice, they will become better at math and we can help them with the hurdles along the way and we can encourage them and cheer them on!

Tip for Parents: Encourage your kids to keep working hard on concepts that are challenging for them. If they say that they are bad at math, talk to them about it and have them change what they are saying to something that is more in line with a growth mindset (such as, I am working hard every week to get better at math!). Talk to your kids about something that you found difficult in school (or in life) but that, with practice, you improved.

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Some of Our Favourite Resources for Middle Years Math Number Skills

One of the best things about being an online learning centre is that we have access to so many great resources at our fingertips! We love videos and games about math (and other subjects), and lately we put together some resources for middle years math number skills. Be sure to check them out, because they are great!

One of the best things about being an online learning centre is that we have access to so many great resources at our fingertips!

We love videos and games about math (and other subjects), and, recently, we put together some resources for middle years math number skills. Be sure to check them out, because they are great!

Multiplying 2-Digit Numbers and 3-Digit Numbers by 1-Digit Numbers

Division of a 3-Digit Number by a 1-Digit Number

Creating Sets of Equivalent Fractions

Comparing Fractions with Unlike Denominators

Improper Fractions and Mixed Numbers

Converting Fractions to Decimals

Understanding Fractional Percentages

Understanding Decimal Percentages

Addition and Subtraction of Positive Fractions and Mixed Numbers with Like and Unlike Denominators

Multiplication and Division of Fractions and Mixed Numbers

Ratios, Rates, and Proportions

Multiplying 1-Digit Whole Numbers by Decimals and Dividing Decimals by 1-Digit Whole Numbers

Operations with Decimals and Making Use of the Order of Operations with Decimals

Addition and Subtraction of Integers

Divisibility Strategies for 2, 3, 4, 5, 6, 7, 8, 9, and 10

Understanding the Square and the Principle Square Root of Whole Numbers

Multiplying and Dividing Integers

Factors and Multiples of Numbers Less than 100, Relating Factors and Multiples to Multiplication and Division, Determine and Relate Prime and Composite Numbers

Demonstrate Understanding of the Order of Operations on Whole Numbers

Mental Math

Middle years math students often also struggle with word problems, so be sure to check out our article about strategies for solving word problems!

If you have any resources that you would like us to add, or if you would like us to help you find resources on a specific topic, feel free to contact us!

We can provide math assessments to find the gaps in your students’ math education, provide resources to help fill them in, and work with your student to fill them in - so they can be successful in their current math classes and future math classes! Assessments are conducted during individual sessions.

Remember that we can help students with various subjects (not only math), in both English and French! If you need help for your student, book a session with us!

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Strategies for Solving Word Problems

We are very experienced at helping students learn the steps to solve math problems and to gain practice and confidence in solving math problems, in both English and French! Be sure to book a tutoring session if you have a student who struggles with math problems in English or French.

We are very experienced at helping students learn the steps to solve math problems and to gain practice and confidence in solving math problems, in both English and French! Be sure to book a tutoring session if you have a student who struggles with math problems in English or French.

Many students struggle with word problems, but here are some tips to help:

The First Step - Read the Problem

The first step when solving a word problem in math is to read the word problem. At this point, students should not even think about how they will solve the word problem, and they should just read the math word problem as though it were a story. They should make sure that they know what all of the words in the word problem mean and, if they do not, they should use a dictionary or the internet to find the word’s meaning, or if they are stuck they can ask an older sibling, a parent, a teacher, or someone else they trust to help them. We repeat, at this point, they should not even think about it having anything to do with math, they should just read it like they would read a story, and make sure that they understand all of the words in the word problem.

The Second Step - Understand the Problem in a Mathematical Sense

The second step when solving a word problem in math is to understand the word problem in a mathematical sense. They should determine what information they have, whether any of it is extra information they do not need, and figure out what the word problem asks them to find. Sometimes, it is helpful for students to make a list of information they are given, cross out any information they are given that is extra information they do not need, and make a list of information they need to find.

The Third Step - Make a Plan to Solve the Word Problem

By the time students reach the third step, they should know (from completing Step 2) what information they have and what they need to find. In the third step, they make a plan of how they will solve the word problem. Sometimes, for fairly simple word problems, the plan can be as simple as performing a mathematical operation (such as addition, subtraction, multiplication, or division). For more complex word problems, a more strategic plan to solve the problem can be made. This can involve strategies such as proportional reasoning, finding a pattern, drawing a diagram, solving a simpler problem, or even acting it out!

The Fourth Step - Solve the Word Problem

Students should now carry out the plan they made in the third step and solve the word problem. Suppose their plan was not effective for solving the word problem. In that case, they might need to revisit Step 3 and make a new plan, or they might even need to revisit Step 2 if they missed a necessary piece of information, or Step 1 if they do not understand one of the words in the word problem. This is when perseverance is needed and, if stuck, some help from a teacher, a parent, or an older sibling, for example.

The Fifth Step - Check the Answer

One awesome characteristic of math is that there is almost always a way to check your answer!

We always tell students that, usually, the students who earn the highest marks on math tests (or, actually, any tests) keep their tests for the longest time and check and double-check their work! We encourage students not to think that the students who hand their tests in very quickly know all the answers and will earn the best marks - because it is, quite often, the opposite of that!

While how the answer can be checked depends on the word problem, a few common ways that the answer can be checked are to perform the opposite operation (for example, addition and subtraction are opposite operations, so if the word problem was solved by using addition, then subtraction can be used to check that the addition was done correctly, and multiplication and division are opposite operations), to estimate the answer and check that the answer obtained is close, and to plug the answer in for the variable if variables were used in solving the word problem.

If the answer is wrong, the student should analyze why their answer is incorrect (they might need assistance). Depending on the reason for which their answer is incorrect, they might need to return to Step 4 and solve the problem again (if they made a calculation error, for example), or to Step 3 and make a new plan (if their plan was not the correct strategy), or to Step 2 (if, for example, they missed an important piece of information), or to Step 1 (if they do not understand one of the words in the problem).

After the student has checked the answer and determined that it is correct (or at least reasonable), the student should write the answer the way their teacher expects it to be written. Some teachers want complete sentences, while others are fine with just one word that states what the answer is (for example, 15 cookies).

Here is an example of Solving a Word Problem by Using these Steps

The word problem we will solve:

Mr. Sand is going on a trip to the beach. The total distance to the beach is 263 km. His car has a 60 L gas tank and can travel 640,000 m on that tank of gas. Suppose that there are two service stations available to Mr. Sand. Station A charges $1.60 per litre of gas, while Station B charges $1.70 per litre of gas. Determine the cost of the gas for his trip if he fills up at Station A versus the cost if he fills up at Station B. Which is more economical?

The First Step - Read the Problem

We read the problem and we discover that we are not sure what the word economical means. Therefore, we can look up the definition of economical online and learn that it means giving good value or service in relation to the amount of money, time, or effort spent. So, we now know that the word economical means the least money spent.

The Second Step - Understand the Problem in a Mathematical Sense

We can make a list of the information we were given and the information we need to find:

Information We Were Given
The distance to the beach is 263 km.
The car can travel 640,000 m on 60 L of gas.
It costs $1.60 per litre of gas from Station A.
It costs $1.70 per litre of gas from Station B.
Is any of this extra information that we do not need? No, we need all of this information.

What We Need to Find
The number of litres of gas he will need to get to the beach.
The cost of his gas for the trip if he fills up at Station A.
The cost of his gas for the trip if he fills up at Station B.
Which option (Station A or Station B) is more economical. (We already know this is Station A because gas costs less per litre at Station A than it does at Station B.)

The Third Step - Make a Plan to Solve the Word Problem

We can convert the number of metres he can travel on 60 L of gas into the number of kilometres he can travel on 60 L of gas, then we can divide the number of litres by the number of kilometres to get the number of litres per kilometre. Then, we can multiply the number of litres of gas required per kilometre by 263 kilometres (the distance to the beach). Following that, we can multiply the number of litres of gas needed to travel to the beach by the cost per litre of gas at Station A, by the cost per litre of gas at Station B, and compare the results to determine which station is the more economical choice (however, since the cost of gas is less per litre at Station A than it is at Station B, we already know that Station A will be more economical).

The Fourth Step - Solve the Word Problem

We follow the steps in our plan to solve the word problem, so we start by converting the number of metres he can travel on 60 L of gas into the number of kilometres he can travel on 60 L of gas: 640,000 m/1,000 m/km = 640 km

Then we divide the number of litres by the number of kilometres to get the number of litres per kilometre:

60 L/640 km = 0.09375 L/km

We multiply the number of litres per kilometre by the number of kilometres he must drive to get to the beach to get the total volume of gas required to travel to the beach:

(0.09375 L/km)(263 km) = 24.65625 L

We multiply that number of litres by the cost per litre of gas at Station A:

(24.65625 L)($1.60/L) = $39.45

We multiply that number of litres by the cost per litre of gas at Station B:

(24.65625 L)($1.70/L) = $41.92 (rounded to the nearest cent)

We can see that the cost of the gas is less at Station A than it is at Station B. Next, we will go one step further than the problem asked us to, and we will determine how much he will save by purchasing the gas at Station A instead of at Station B:

$41.92 - $39.45 = $2.47

The Fifth Step - Check the Answer

We can check that we converted the distance from metres into kilometres correctly by converting the number of kilometres into metres and determining whether we get the number with which we started:

(640 km)(1,000 m/km) = 640,000 m

Yes! We get the number with which we started!

We can check that we found the number of litres per kilometre correctly by multiplying the number of litres per kilometre by the number of kilometres and determining whether we get the number of litres with which we started:

(0.09375 L/km)(640 km) = 60 L

Yes! We get the number of litres with which we started!

To verify that we got the correct number of litres of gas that will be required to travel to the beach, we can divide the number of litres required by the number of litres per kilometre and determine whether we get the number of kilometres he must drive to get to the beach:

24.65625 L/0.09375 L/km = 263 km

Yes! We got the number of kilometres that he must drive to get to the beach!

To check that we got the correct cost for buying the necessary number of litres of gas from Station A, we can divide the total cost of the gas by the cost per litre of gas at Station A and determine whether we get the number of litres that are required:

$39.45/$1.60/L = 24.65625 L

Yes! That is the number of litres that are required!

To check that we got the correct cost for buying the necessary number of litres of gas from Station B, we can divide the total cost of the gas by the cost per litre of gas at Station B and determine whether we get the number of litres that are required (approximately, since the total cost of the gas from Station B was rounded to the nearest cent):

$41.92/$1.70/L = 24.6588 L

While this result is not the exact number of litres that are required, we know that we had rounded the total cost of the gas from station B to the nearest cent, and 24.6588 L is very close to 24.65625 L, so we are confident that our answer is correct.

We knew, based on the price per litre, that Station A would be more economical than Station B. We can also check our answer by finding the difference in the cost per litre of gas at Station A and the cost per litre of gas at Station B and then multiplying that difference in cost by the number of litres required to determine whether the amount that we calculated he would save by buying the gas at Station A instead of at Station B is correct:

$1.70/L - $1.60/L = $0.10/L

($0.10/L)(24.65625 L) = $2.47 (rounded to the nearest cent).

Yes! Our answer is the amount of money he would save by buying the gas at Station A instead of at Station B!

Finally, we write a sentence that answers the questions we were asked:

The cost of buying the gas necessary from Station A to drive to the beach is $39.45 and the cost of buying the gas necessary from Station B to drive to the beach is $41.92. Therefore, buying the gas from Station A is more economical, and he would save $2.47 by buying the gas from Station A.

Have fun at the beach, Mr. Sand!

Want resources to help with reviewing middle years math number skills? Check out Some of Our Favourite Resources for Middle Years Math Number Skills!

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