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Alex Smith's avatar

Hi, Alex, Curriculum Director of Math Academy here.

After some reflection, I decided to respond to this.

TLDR

* Math Academy is a work in progress (hence why we're still in beta).

* Do we avoid or skip the teaching of concepts? No, certainly not!

* Could we do more to ensure conceptual understandings are hitting home? Absolutely.

* Can anything be done to ensure that a larger proportion of 4th-grade students can benefit? For sure.

* Is Math Academy fundamentally broken and cannot be fixed? GTFOH!

Long Form

I cannot post as a single comment, so it must be done as a series of comments.

While the author raises a few reasonable points, it's nothing we're not already aware of. Also, it's self-evident that the author had no intention of properly engaging with the platform.

It's not my intention to go through the review line-by-line and comment on every point. However, some points about the author's perspective on education stood out for me.

> Good teachers don’t sit around and watch kids read. They ask probing questions. They ask for explanations. They build understanding.

Not quite. When a good one-on-one tutor introduces a new concept to a student, they might start with some (very) short motivation. Then, they'll introduce a worked example, as simple as possible to start, and carefully walk through the solution, invoking prerequisite ideas where necessary and using their knowledge to anticipate where the pain points in the solution process might be. They show them how to solve the problem and then get the student to demonstrate their understanding by solving similar problems.

Introducing a concept for the first time is usually not the time to ask "probing questions." It's way too early for that! The student only learned what the hell a quadratic equation was two minutes ago, and you're already probing them! Give them a chance to internalize some information first!

So, go through 1-2 worked examples and check that they understand by having them solve some similar problems. Once they've gotten the hang of that, slightly increase the complexity of the problem. Do that 2-3 times, and you'll come away with a student who's had a happy and satisfying learning experience!

Most students struggling with a new idea don't want to be probed for understanding every two seconds. If anything, too much probing too early could undermine their confidence entirely. Now, that's not to say students shouldn't be probed. But give them a chance to get familiar with the material first. Once they're happy, confident, and have reached a certain point in their understanding, *then* you can challenge them.

Unlike most users, I feel the author did not make a genuine effort to engage with the product. Quote:

> Given the choice, most people will skim over technical explanations... I was no different.

Actually, no. Most people genuinely interested in learning new material are willing to spend some time reading information about what they're trying to learn! (I'm assuming we're talking about more mature students now). Surely, it's not gotten to the point where we're discouraging reading to learn!

Granted, technical discussions can be difficult to wade through, at any level. I sympathize. But this is why we break a course down into hundreds of individual topics, which are themselves broken down into multiple stages. The cognitive load (i.e., the amount of new information that requires storing in working memory) at any one point during the learning experience is designed to be as low as possible.

The author raises a reasonable point: getting some 4th-graders to read text and learn from it is nigh impossible. This could be for a variety of reasons. We've never claimed that our 4th-grade course *in its current form* will work for every 4th-grade student, and admittedly, it's down to us to do more to make that dream a reality. But with all that said, our 4th-grade course currently has a 93% completion rate (meaning, 93% of students on this course mastered *every single topic*!), and 99% of lessons are passed within two attempts (coincidentally, 93% of lessons passed within the first attempt). So there's no doubt that *some* 4th-graders can read the material, learn from it, and consequently get tremendous value out of the product.

It's our job to widen the net to make the course as inclusive as possible. However, far from being an unfixable problem as the author suggests, technical solutions that are already in the works are possible, such as:

* In-task analysis (figuring out exactly what students are doing while using the platform and taking steps to intervene if they slack or goof off).

* In task-coaching, using the in-task analysis data (basically guiding the students on how to use the system correctly).

* For younger students who have difficulty reading text, videos and/or animations are always a possibility.

The in-task analysis and coaching are technically challenging. You'll need to figure out what the student is doing in real-time and respond accordingly, just like a teacher or tutor would. But these things are certainly not impossible. We're already on it!

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Andrew Duval's avatar

Thanks for the review, Michael. I’ve noticed some of the recent MA developer posts, so I was keen to check it out. I’m surprised because I thought this would be right up your alley (and so did you, I guess?).

But I so wonder how much of your assessment is about a disagreement between how “conscious” to make a particular act of learning?

It’s been ages since I read your book, but if I remember correctly, you like to use examples to stimulate thought, reflection, and analysis prior to doing a procedure—is that right?

But you can also use examples to build a kind of mental muscle memory without ever really making the learner aware of it, until you choose to bring something to their awareness “wax-on, wax-off” style. That approach requires a lot of volume, so you want to make each individual task as quick as possible to get enough reps.

(I reckon both approaches are valid and not mutually exclusive—you can alternate—but if you are making a product, you probably have to choose one or the other, at least to begin with, simply because of time and budget constraints.)

Based on your review, MA sounds intentionally like a high-rep, high-speed, low-reflection way to build muscle memory, which is good for trivialising procedures and making other conceptual instruction easier. Does that sound fair? Am I missing the point? (Maybe I should just read their manifesto and not dump these questions on you! 😅)

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