What happens when you pass a math course but still don’t feel ready for the next one?
And what do you do when the skills you need to be working on are so far behind you that no one’s even talking about them anymore?
This is Liam’s story.
Liam started tutoring with me in the fall, just before beginning Grade 10. His course was Pre-Calculus and Foundations 10, and it was scheduled to run for five months. It moved fast, and from the beginning, Liam made it clear that he wanted to stay focused only on the Grade 10 material.
Very early on, I noticed that he was struggling with math concepts that should have been solid by middle school. But no matter how gently I tried to bring it up, he didn’t want to go back and review. Even when there wasn’t an upcoming test, he was determined to stick with the current curriculum and keep moving forward.
So I followed his lead.
I helped with the Grade 10 content, even though it was clear he was having trouble keeping up. There were big gaps in his understanding, and layering new material on top of that just wasn’t working. Still, this was the path Liam chose, and I did my best to support it.
As the course drew to a close, I assumed our time together was also coming to an end. I figured he would finish the class, see how difficult it had been, and choose Foundations of Math 11 (math for students not studying science, engineering, or business) for his next step.
But when I contacted his mom to confirm our end date, her response surprised me. She explained that Liam would be continuing with tutoring over the summer and would be enrolling in Pre Calculus 11 (BC curriculum) next.
That changed everything.
Pre-Calculus 11 is a significant leap, and based on what I had seen throughout the school year, I knew he wasn’t ready for it. His teacher had actually recommended Foundations 11 instead. However, his family wanted to keep more doors open, especially since Liam had been thinking about going into business or a field that might require stronger math.
Although Liam had passed the course, his foundational skills were still weak. Some of the gaps I had seen went all the way back to Grade 6. He didn’t yet understand how much this would impact his ability to succeed in the next course. And while his parents were aware that math had always been a challenge, they may not have realized how deep the issues really ran.
Going into summer, our new goal was to get him as ready as possible for the course ahead. By that point, I had already been trying to point out areas where his understanding was shaky, hoping he might become more open to reviewing earlier material. So I asked him what he thought we should focus on over the summer. He gave a little shrug and said, “Whatever you want.” He knew I was going to choose what I was going to choose anyway.
I interpreted his response to mean that he wasn’t sure what he needed, but he was open to letting me guide him. We finally had a starting point.
We had a rhythm to our sessions. He would work through questions, take a short break around the halfway mark, and then return to finish the lesson. He had been asking to “go to the bathroom” in the middle of nearly every session since we started working together.
Eventually, I realized those breaks weren’t always about needing the bathroom. They were a way to step away when the material became too frustrating or mentally draining. So I began building in breaks more intentionally, especially when I could tell he needed a reset.
Homework brought its own challenges. He often started it right before our lesson, sometimes with just fifteen minutes to go. Since we work on a live whiteboard, I could literally see him begin the assignment before the session was to start. That didn’t always give him enough time to finish properly or reflect on what he was doing. We’re still working on building better habits around that.
Despite the slow pace, we kept going. I began introducing concepts I had known were missing since the fall. Some of those gaps went all the way back to middle school. Because I don’t typically teach younger grades, I had to experiment with different ways to explain things clearly.
Improper fractions were one of the first major hurdles. He didn’t understand what five-fourths meant or how it was different from four-fifths. I’m sure his teacher had taught it at some point, but maybe he didn’t fully get it at the time, didn’t ask for help until it clicked, and hoped the concept would disappear.
I tried the conventional explanation: 7/4 means each whole is made up of 4 pieces, and you have 5 pieces of that size. That did not work. So I approached it differently.
I asked him to draw a circle and divide it into four equal parts, shading one section to show one-fourth. Then I had him copy and paste the image until we had 7 of them. I asked him to move all the shaded pieces into one circle until it was full. Once he saw that one circle was filled and three piece remained, the idea of seven-fourths finally made sense.
As summer continued, I looked for ways to make the math feel more connected to his life. Liam had always struggled to see why any of this was useful. He often asked why we needed to learn certain things, and I could tell that he was hoping my answer would confirm his belief that math was pointless.
Of course I didn’t give him that.
So I leaned into what was relevant to him. While he was on vacation in Hawaii, we continued tutoring. His family changed the lesson time to account for the time zone difference, but we didn’t miss a beat.
During those sessions, we started working on unit rates. One of his homework assignments was to find real-world examples of unit rates while he was out and about. He took photos of a fruit stand, speed limit sign, and a gas price sign, uploaded them to the whiteboard, and we used those images in our lesson.
Together, we calculated things like cost/lb, mi/hr, cost/gallon, and then compared those prices to Canadian equivalents. This gave us a natural way to use cross-multiplication as a tool to convert units and compare values. We discussed exotic fruit and the cost of living in Hawaii vs. Vancouver.
That got his attention.
At times, he would make quick estimates on his own, without being prompted. When he saw “1L = 0.264172 gallons,” he said, “So there are about 4 litres in a gallon.” These kinds of rough calculations helped him make sense of the quantities. He was starting to use math to understand the world around him.
Since Liam was thinking about studying business, I wanted to connect what we were learning to something that would actually matter in his life. We were working on linear functions, and I saw an opportunity to apply y = mx + b to university tuition.
I asked him to choose a few real schools he might consider attending. We looked up tuition information and figured out the cost per course, which became our “m”, the rate. Then we grouped all the other student fees together as a fixed cost.
This is an oversimplification, I know.
I just wanted him to see how the equation could model something real. So if one course cost $600, and the fixed fees added up to $1,200, we wrote the equation as:
y = 600x + 1200
Here, x represented the number of courses, and y was the total cost of tuition. He calculated the cost of a full course load for the first year. He was engaged.
And honestly, what Grade 10 student wouldn’t want to know how much university might cost? The questions he asked were more thoughtful. The work felt less abstract than “slope” and “y-intercept.” And the formula finally had a purpose beyond just getting the right answer.
There are still frustrating days. Liam hasn’t suddenly turned into the ideal student. But something changed this summer in how we worked together.
Some sessions didn’t go anywhere until we stopped talking about math entirely. I never planned on those tangents, but they were necessary to move forward.
One time, I told him about a figure skating lesson I had. My coach kept telline me to have, “pointed toe,” again and again. I tried to do that but it seemed that I wasn’t doing that. Finally I asked, “Where am I supposed to point it?”
She didn’t realize I didn’t understand that “pointed toe” was a thing.
I shared that story with Liam and said, “I’ve probably done that to you in math. I’ve told you to do something without realizing you didn’t know what I meant.” He laughed. He knew exactly what I was talking about.
Another time, he came to a session having skipped his homework again. We couldn’t keep going like that. So I stopped and asked him how he currently felt about math and what his goals were.
“Other than your mom telling you that you need to do summer tutoring, why are you doing summer tutoring?”
Like many teens, he didn’t have a well-defined goal. He knew he had to get better at math, but he didn’t know what that looked like or where the goal post was.
We discussed what successful students do.
Liam: That’s a lot of commitment.
Me: I know. That’s why I ask how badly you want this.
I wasn’t asking him that to pressure him. It is entirely possible to be successful and make lots of money entering other professions. If he wanted to go into something that required math, then that decision was all his.
Earlier in the year, he would avoid asking questions. If something was wrong, he would just guess again and hope I’d let it slide if he got the right answer.
Lately, that’s changed.
Now he brings me the things he’s unsure about, even if they seem basic.
He’s trying to understand math even if he didn’t understand it before.
He knows asking such questions is highly encouraged.
That kind of trust and change in mindset took time.
School is starting soon, and Liam isn’t walking into Pre Calculus 11 (BC curriculum) fully ready.
There’s still work to do, and we both know it. But he’s coming in with more understanding, more willingness to ask questions, and a better attitude toward learning.
I’ve already told his mom that no matter what happens this summer, Precalculus 11 won’t be easy. There’s no quick fix when the foundation has this many cracks.
But he’s in a better place than he was in June, and we’re continuing twice a week to keep building.
Tutoring doesn’t follow a straight path.
I can prepare lessons and make learning plans, but every student brings something different, and I have to respond to what’s in front of me. This summer, we had to figure it out as we went.
Somehow, through all the bumps and detours, we made real progress.
How the Pre Calculus 11 (BC curriculum) test results will look because of the time we spent on summer tutoring, I don’t know. The foundation still has holes, and you can’t patch that up in one summer.
But these are the improvements I noticed:
He is asking questions to clarify his thinking.
He is more open to reviewing what he finds difficult.
He has better awareness of what it means to be a successful student.
He is using math to understand real situations.
He is writing clearer, more communicative solutions.
These are the kinds of skills that matter more than most people realize.
If you’re only looking at grades, you might not see a huge change that says, “Tutoring was definitely successful.” But the real work doesn’t always show up on a report card.
If your child is feeling lost in Pre Calculus 11 (BC curriculum) or struggling with confidence in math, there is a way to fix this.
Contact me today to start a conversation that can change the school year.
