Helping Your K-8 Kid Learn Math

As many school districts plan atypical scenarios for the Fall, many parents are asking a couple important questions:

1. If I want to homeschool, what curriculum should I use?
2. If my kid is still "in" school, but doing a ton of work independently, how can I help them?

Choosing a Math Curriculum

Actually, I wish more people would ask what curriculum they should use. Many intelligent people imagine that they can just do it themselves or buy a book off amazon and get it done. It's not that simple. Curriculum matters, but where should you turn?

In 2012, New York state commissioned the creation of a really great set of curricula for K-8 Math and English Language Arts (ELA). The result of that effort is EngageNY, which is generally considered some of the best open education resources (OER) out there. When that contract wound down, part of the team that created EngageNY decided that they were not done, so they created UnboundEd.

UnboundEd has updated and extended the EngageNY product to create solid content with good focus, rigor, and coherence. Oh, and it's free. They are also really great people who care deeply about equity and confronting our implicit biases. For proof, check out their Bias Toolkit. 

For another perspective for grades 6-8, check out Open Up Resources. Open Up is newer, and perhaps less robust, but they have some good stuff.

There are other options. EdReports.org has reviews of many curricula, so you can certainly poke around there. That said, you could do a whole lot worse than leaning heavily on UnboundEd and sprinkling in a few things from Open Up (grades 6-8) and/or the supplemental resources listed below.

Getting Math Help

What if you or your student gets stuck on some math topic? Note that this is a really different need (and set of solutions) from the curriculum focus above.

1. If you haven't checked Khan Academy, you haven't done a serious search. I would not use this as a curriculum, but the videos can help a learner get over a bump in the road, or can help a parent brush up on something they learned and forgot years ago.
2. BrainPop is another good source of videos. There are a ton of others, and you can find many at OER Commons.
3. Friends and family could help. Who do you know that is good at math? They are likely sitting at home, and would be happy to help and interact with someone new. Lean on your network!

Having the Right Mindset

Stop telling kids that they are bad or good at math. Carol Dweck and others have done and published a ton of research on this, but the core idea is that with VERY few exceptions, most people can become good/better at math if they put in the right effort. Instilling a static mindset by telling a kid s/he is good at math or bad at math takes away their agency. They need to know that effort is valuable and it can lead to getting better.

This isn't about participation trophies and orange slices. This is about rejecting the dysfunctional and wrong idea that our genetics have predetermined what we can be. This is about helping every student know that progress is important and within their control. Lifting weights doesn't inherently make you strong, but with the right program, effort, and persistence, a lifting program can help you build muscle. It's the same way with mental effort helping our math ability grow.

Helping Your Kids Keep Learning: Math

As many school districts close for the remainder of the academic year, many parents are struggling with several issues:

1. If the teacher isn't doing much, what should I have my kid(s) do?
2. What are some good resources for math curriculum?
3. What are some good resources for math help?

What Matters Most?

A: Not losing ground. Studies show that students lose a fair amount of ground in the summer. Imagine a summer that lasts 5 months instead of 2.5! Therefore, I really care about progress. Get them to do something that is close to grade-appropriate. I just don't want them to forget how to do math.

B: Being ready. This is tougher to do, but if a student is taking a course now that has foundational content for next year's course, then I care about those foundational skills and concepts. The trick is identifying those key things. Achieve the Core has really helpful Focus documents for each grade. Look for the solid green squares. These are particularly helpful for anyone in a Common Core state. It's not always so easy to identify the key foundation content, so you might need to reach out to a teacher or curriculum person for guidance. One of the important things to keep in mind is that not everything is critical. You don't need to jam it all in there. Pick and choose carefully.

C: Liking math. If your approach to being ready results in a student who hates math, then you've created problem. I know this is tough, but you need to find a way to keep them moving forward that doesn't spoil whatever affinity they have for math. Not losing ground is more important than being ready, and liking math is perhaps most important.

Math Curriculum Resources

If you are pretty much on your own for helping your kid move forward with math, consider going to UnboundEd and/or OpenUp. They have solid content with good focus, rigor, and coherence. Please avoid entering the wild west that is Teachers Pay Teachers. TPT has a ton of issues I won't go into, but suffice it to say that I'm not a fan.

Math Help

What if you or your student gets stuck on some math topic? Note that this is really different need (and set of solutions) from the curriculum focus above.

1. If you haven't checked Khan Academy, you haven't done a serious search. I would not use this as a curriculum, but the videos can help a learner get over a bump in the road.
2. BrainPop is another good source of videos. There are a ton of others, and you can find many at OER Commons.
3. Friends and family could help. Who do you know that is good at math? They are likely sitting at home, and would be happy to help and interact with someone new. Lean on your network!

Progress is important, but don't stress anyone out. The current state of affairs is inherently stressful, and math shouldn't be part of the problem. I hope math can be part of the solution -- doing some math work could fit as part of a new daily structure that provides some semblance of consistency and normalcy. 

The Cattle Drive: Too Much Calculus

Reading Pamela Burdman's piece at Hechinger Report: Numbers evoke joy and wonder, why doesn’t math class? got me thinking.

I have already argued that we push too many kids to Algebra too early. Now to complain about the other extreme.

High school students are often driven like cattle through their math courses. Those who can withstand the cattle drive make it to the fertile pastures of calculus. Sadly, many of the herd don’t make it and are left along the side of the trail.

Not every student belongs in calculus. Though students who plan to be engineers, physicists, mathematicians, or economists need calculus, many others have abilities or interests that make them better suited to other mathematical destinations. The cattle drive hurts kids who lose interest in a destination they don’t care about.

Don't get me wrong: I love calculus. It is beautiful, useful, fun stuff, but it isn't for everyone. Everyone should master Algebra, but not everybody needs to master calculus. And honestly, many of the topics in Algebra II only exist to prepare students for calculus. This doesn't mean creating a dumbed-down track, but maybe there are other options for rigorous pathways.

Why not map out different mathematical pathways for different kids? After Algebra I, maybe some kids would be better served by courses in discrete math, probability, statistics, logic, or some other mathematical topics. Ideally, students would be able to switch back and forth between pathways if enough foundational skills were shared between parallel courses.

I know I'm tilting at windmills, but I'd like to see the cattle drive identify some other destinations; there is lots of interesting, useful math out there. Too many people think they hate math because they hated the cattle drive they were on in high school.

Early Algebra: Crushing Kids

Some states want to get all their students to take Algebra by the end of grade 8. The idea is that this will provide equal access to challenging curricula.

The Washington Post's Jay Matthews discussed the issue in Recalculating The 8th-Grade Algebra Rush and the original report is available here: The Misplaced Math Student: Lost in Eighth-Grade Algebra.

I'm a fan of Algebra and a fan of helping as many students as possible master it, but I am not a fan of aggressive time lines for when it has to get done. Pushing all 8th or even 9th graders into Algebra is a problem. Kids who are not ready for Algebra would be better served by shoring up their math foundations. They need number sense, especially when it comes to decimals and fractions. Students who are pushed into Algebra before they are ready are doomed to fail and are probably doomed to hate math forever. I don't want them to take silly math classes that lack any rigor, but I don't want to throw them into classes for which they are not prepared.

At the other end of the spectrum, there is also a push to get good math students to take Algebra in seventh grade or even earlier. Not every kid is ready for Algebra in eighth grade. Very, very few kids should be taking Algebra before eighth grade. If a kid is that good at math, why not provide a more rich mathematical curriculum for the kid instead of just having them rip through the same old courses more quickly?

As you might imagine, my reaction to the title of Jill Barshay's article in the Hechinger Report: Gifted classes may not help talented students move ahead faster was a resounding "good!"

Some of my issues with the "hurry up and go fast" approach to gifted math education:

1. I have heard SO many stories of kids who took Algebra in seventh grade and ended up losing interest before their senior year. This is anecdotal, so I need to find solid data.
2. There is solid evidence to support the existence of the Protege Effect: Students who teach their peers deepen their own understanding of skills and concepts. Many parents of precocious students complain that their kids are being held back and doing the teacher's work, but those peer teaching experiences are deepening both students' knowledge.
3. Teachers at every level complain about students who have zoomed through prerequisites without really understanding everything they need to understand to prepare for later study. For almost all students, that zoom through leaves gaps.
4. Emphasizing extrinsic outcomes can quash student motivation and long-term interest. Being accelerated can be one of those extrinsic outcomes that push students for a while at the cost of  their own intrinsic motivations to learn.

As Barshay indicates:

"... Research points to the lack of consensus on what the goals of gifted education should be. Many don’t think it should be about advancing students as quickly as possible. High quality instruction that helps kids who’ve already mastered the basics go deeper into the material may ultimately be beneficial. And annual state assessments may not do a good job of measuring this kind of depth, creativity or critical thinking."

Algebra is a good thing. I value its abstraction and generalization and problem solving, but let's make sure that the kids who take it have the right foundation and that it really drives deep learning and affection for math.

Khan Revisited

A while ago, I wrote The Wrath of Khan (one of my favorite blog post titles).

What's changed since then? Quite a bit. First of all, Khan Academy (KA) is now the 400-lb gorilla of the free online instructional video space. Everyone knows them. I have spoken to several educators who have built courses that rely on heavy, daily doses of KA, but I also know others who seem to use Khan as an epithet. At times, it seems that KA is a bit of a pedagogical Rorschach test: How you view KA can say quite a bit about who you are as an educator.

My earlier post went into some of my concerns about KA, so what about some of the positives?

1. KA's integrated assessments help students see their progress. 
2. All of their content is free, pretty comprehensive, and generally fairly solid. 
3. One really interesting thing Khan has done is partnering with the folks at The College Board to provide customized SAT practice. They even have solid data that indicate the practice helps students raise their scores. Free SAT prep that actually shows improvement! Every HS student should be using this.

Khan isn't perfect, and can be over relied upon, but they are providing valuable services for free, and that's pretty great.

Blogs Worth Reading: Math Teachers

I have found a group of math teachers who have made a really strong online community. Together, they are questioning, innovating, and making positive change happen and then sharing through blogs and tweets. It's incredibly inspiring.

Honestly, this is the best use of blogs and Twitter I have seen yet. My favorite thing about all of them is that they clearly have a growth mindset when it comes to their craft. They are growing as teachers in a collaborative, sharing way.

Anyone who is a new math or science teacher should read these blogs and follow these folks on Twitter.

That said, here is a list of some of my favorite math teacher bloggers/twitterers.

Kate Nowak (@k8nowak)
Blog: f(t)
Not only does Kate solicit ideas from the twitterverse; she actually puts the ideas into action and shares the results (regardless of how successful they were).

Sam Shah (@samjshah)
Blog: Continuous Everywhere but Differentiable Nowhere
Sam's post on the Blogotwitterversphere is great.

Fawn Nguyen (@fawnpnguyen)
Blog: Finding Ways
Great sharing, especially with the 3Acts.

Geoff Krall (@emergentmath)
Blog: emergent math
A nice mix of real-world application-driven stuff as well as insightful commentary.

Check these people out. I find them all to be informative and inspirational. I know there are others who are really good (my list of a few thought leaders who are not in the classroom will follow in a later post), but these are quite good. If you know of other great ones, please share.

Zoran Popovic: He's Got Games

This is the first in an occasional series on researchers I think are doing interesting work. Some will be well-known, but others might be somewhat less so. Regardless, I will share some thoughts on why more people should be putting this person's research into action. These aren't researchers who would only be interesting to someone working in an ivory tower. Each one does interesting work that you could use.

Dr. Zoran Popovic does a lot of work, but one thing he does really well is make games. As a matter of fact, he worked on algorithms that are used in the video game Destiny. He also cares quite a bit about how to help students. Notably, how to use hints to help students learn.

A Few of His Projects

Dr. Popovic runs the Center for Game Science at the University of Washington. CGS has done a bunch of good stuff including:

• FoldIt provides a context in which people with no knowledge of biochemistry can solve complex protein structure problems that help scientists solve real problems. It's actually pretty darn remarkable.
• Refraction is an interesting (and effective) way to learn fraction concepts and operations.
• DragonBox allows (even very young) students to learn algebra.

Popovic also runs a non-profit called EnLearn, which has built an adaptive learning platform. The EnLearn platform is not designed to replace teachers. It's designed to help them be more effective.

My Favorite Popovic Idea

So much to choose from, but I'm going geeky. I really like his Trace-based Framework for Analyzing and Synthesizing Educational Progressions. This reminds me of the Knowledge Spaces idea that lies behind ALEKS. It's computational and theoretical, but when you see it described well, it makes total sense. To a great extent, these traces are a big part of why EnLearn is so powerful.

Many people are making educational games and some people have built adaptive learning platforms, but very few people are doing either as well as Dr. Popovic and his teams.

Math Illiteracy

On his Uncertain Principles blog, Chad Orzel provides an interesting look at the problem of our culture's math illiteracy in The Innumeracy of Intellectuals. Professor Orzel's essential point is that people are generally ashamed of a lack of knowledge about art or culture, but can have a sense of pride about their lack of mathematical knowledge.

I don't think that everyone needs to love math any more than everyone needs to be an artist or a musician. On the other hand, here are three reasons I think everyone should master some key mathematical skills and concepts:

1. Math matters: We are constantly bombarded by information and much of it requires some analysis. Sometimes, we need a solid grasp of logic, and at other times, we need to understand statistics or probability. Math helps us make sense of many situations.
2. Math is helpful: The more math you know, the more ways you can see that it can be helpful as a way to solve real-world problems.
3. Math is beautiful.

Point 1's implications: I think everyone needs some knowledge of algebra, probability, and statistics. That's it. No calculus. No trigonometry. Nothing too fancy. If you can't make sense of the data and statistics that are part of modern life, then you can't make good medical, financial, or political decisions.

Points 2's implications: Teachers need to find ways to get students using math that matters and doing math that is just better. Dan Meyer has a post Real Work v. Real World. Doing crappy work in a real-world context is probably worse than doing interesting work in a made-up context. Math students need to do more good work.

Point 3's implication: It just is. If you haven't seen beauty in math, then you are hanging out with the wrong math teachers (everyone hangs out with a bunch of math teachers, right?).

Anyway, math matters, it's helpful, and it's beautiful. We need to use these truths to draw more people in and keep them engaged with learning math.