Cracking Math Mysteries Together
Hey Reader,
Before we dive in this week, I have a quick question for you.
True or false: When a child doesn't understand something in math, the best next step is to assign more practice problems.
Hit reply with True or False — I have a feeling I know what most of you are going to say, and I cannot wait to see if I am right. 😉
LIFE
There is a moment that every homeschool mom knows, and if you have been at this for more than a few weeks, you have almost certainly lived it. You explain a concept, your child nods, you move on, and then two days later they look at a problem that uses that exact same concept and stare at it like they have never seen anything remotely like it in their entire lives.
And the feeling that follows is a complicated one, because it is part frustration and part self-doubt and part genuine worry that something is wrong, either with your teaching, with your child, with the curriculum, or with all three simultaneously.
Here is what I want you to know before we go any further: that moment is not a crisis. It is information, and information is something you can actually work with.
HOMESCHOOL + MATH
Last week we talked about the signs that tell you your child genuinely understands something. This week we are on the other side of that coin, because knowing what mastery looks like is only half the picture. The other half is knowing what to do when the understanding clearly isn’t there yet.
So, let's talk about how to diagnose where your student’s gap actually is, and then talk about what to do about it.
Step 1: Resist the urge to re-explain the same way. This is the most common instinct and also the least effective response to a child who is not understanding something. If the explanation did not work the first time, doing it again louder and slower is not suddenly going to make it make sense. Contrary to our natural instincts, when a child is stuck, the first thing you should do is not re-teach: it should be to investigate, because what looks like one problem on the surface is almost always something different underneath.
For example, let’s say that your child is struggling with adding unlike denominators. You might normally start explaining how to find the common denominator all over again, but instead you do some investigating (see Step 2!). You ask some questions and find out that your student doesn’t understand what a denominator represents, so he doesn’t understand why he has to have common denominators in the first place. The problem wasn’t the procedure, it was the concept underneath it.
Step 2: Ask, don't tell. Before you reteach anything, spend five minutes asking your child questions to find out where their understanding actually breaks down. Start with what they do know and work your way toward the edge of their understanding, because the gap is almost always deeper than the surface. For example, you could ask things like:
- What do we know? It’s okay if you don’t know how to do the whole problem, but where could we start? Why?
- Where does this start to feel confusing — is it right away, or does it get confusing partway through? [walk through each step asking if that particular piece makes sense until you find the breakdown.]
- What does [insert specific part of problem] mean?
- What are some things we know will NOT work?
These questions will tell you more about what your child actually needs than any amount of re-explaining will.
Step 3: Go back further than feels necessary. Once you have identified where the understanding breaks down, go back one step further than that. If your child cannot add fractions with unlike denominators, the gap might be in finding common denominators, but it might also be because they don’t fully understand what a denominator actually represents. This is a much earlier concept than you might expect to be revisiting, but sometimes, it’s the actual terms we use that are the cause of the breakdown. Going back further than feels necessary is not a sign that your child is behind or that you have failed. Instead, going back is the most efficient path to genuine understanding, because a foundation you can actually build on is worth far more than ten lessons stacked on top of a gap.
Step 4: Change the representation. If you have explained a concept one way and it has not connected, the next step is to find a completely different way to represent the idea. You could draw a picture, use physical objects, or relate it to a real-world context that makes the abstract idea something your student can relate to. Different representations access different kinds of understanding, and sometimes all a child needs is to encounter an idea from a different angle before it suddenly makes complete sense.
Step 5: Give it time and space. Now, some concepts just need more than one encounter before they settle into long-term understanding, and that is completely normal and not a problem that needs to be solved immediately! If you have diagnosed the gap, backed up, tried new representations, and your child still seems to be on the edge of understanding rather than mastering it, put the math away. Come back tomorrow with fresh eyes and a short review, and you’ll often find that whatever was causing your student to stumble isn’t as big of a roadblock after the brain has had time to consolidate and ruminate on the previous day’s content.
Say it with me: the goal is not to fix it today. The goal is to tend it faithfully until it clicks!
Speaking of finding the real gap: I just published my first blog post in a long time this week, and it goes hand in hand with everything we have been talking about today and will be talking about the rest of the month! If you have ever wondered whether a curriculum switch might be the answer, I think you will find it really helpful.
Read: Curriculum Change Won't Fix Math Challenges: Here's Why →
GRACE
Paul writes in 2 Corinthians 12:9: "And He has said to me, 'My grace is sufficient for you, for power is perfected in weakness.' Most gladly, therefore, I will rather boast about my weaknesses, so that the power of Christ may dwell in me." (NASB)
His power is perfected in weakness, and I have been sitting with that verse in the context of homeschooling because I think there is something really important about it for the moments when we feel most unqualified, most stuck, and most unsure of whether or not we are doing this right. Let me encourage you: you do not have to have every answer, and you do not have to know instinctively how to reach your child in every hard moment, because the God who designed your child's mind is present in the gaps just as much as He is present in the breakthroughs.
Frame your thoughts in a new way: struggle is not evidence that you are failing. It is in the struggle where the most important growth happens, in you and in your child, and the God who meets us in our weakness does not ask us to be strong before He helps. He just asks us to keep showing up, and to trust that His power dwelling in us is more than enough for every gap we cannot fill on our own.
So — what did you reply at the top? True or false? I have a feeling the answer might have shifted something for a few of you, and if it did I would genuinely love to hear what changed. Hit reply and tell me! 💛
See you soon,
Mrs. Holman
