I began a conversation about Family Math over at PamBarnhill.com. I talked about why it works for us and gave a brief outline of how to make it happen. I promised to share more details here during Math Month. This is me keeping my promise!
Nothing Else Matters
In the previous post, I mentioned how I was helped by a quote from Andrew Kern of the Circe Institute. When thinking about how to teach our children, it isn’t always helpful to think in terms of “grade level”. This can stifle kids who are ready for more and stress out kids (and parents) who need to move at a more relaxed pace. When it comes to deciding what to teach, Kern says …
To what level has my child mastered this skill? And what is next? Nothing else matters.
So, in it’s simplest form, all that you need in order to teach something are the following things:
- A way to assess where your child is now in current understanding and mastery.
- A plan that will tell you what to teach next.
- A guide to help you know how to teach that next thing effectively and then assess (see #1).
For many people, textbooks meet all three of these requirements. And, let me be the first to say, I’m a strong believer in “If it ain’t broke, don’t fix it.” If you use textbooks and they are working beautifully for you, keep at it, my friend! This post isn’t meant to evangelize anyone away from textbooks. It’s meant to answer the questions of what to do (and how to do it) when textbooks aren’t working!
What is Next?
Textbooks can go from being a blessing to being a burden for a number of reasons. One of them might be that your students need a more flexible or hands-on approach. Another might be that you find yourself teaching a bunch of different kids a bunch of different topics and you feel stretched thin as a homeschool math facilitator.
But most of us who want to strike out on our own don’t feel qualified to do that without some kind of scope and sequence, some kind of road map to at least assure us that we aren’t “missing” things, that there won’t be “gaps” in our children’s educations. Here are some ways to get a road map.
- Your old textbooks or textbook series. Many textbook companies publish free PDFs of the scope and sequence for each grade level. Or, sometimes you can look at a free PDF sample of the textbook that will show the table of contents (like this).
- Common Core. I know a lot of folks cringe when they hear about the Common Core. What’s really at the root of the disdain, however, are the ways they are tested and measured. If you just want a list of what somebody thinks kids should learn in each grade, the Common Core is definitely that. It is also very thorough and specific about what is included and what level of understanding is expected with each topic.
- Khan Academy. Khan Academy is aligned to the Common Core, so looking at what is covered in each grade level “Mission” is just another way to get a list of what folks generally teach in each grade.
- The Core Knowledge Series. For each grade level K-6, you’ll find a book titled “What Your ___ (Grader) Needs to Know”. While these books aren’t free, you can probably find them at your local library. Or, if all you want is a quick overview of recommended topics, click on the “See Inside” option on Amazon and scan the table of contents. (These books cover all subjects, not just math, so scan for the section on math, if that’s what you’re after.)
- Math on the Level. It’s no secret. This is my favorite by far. The huge advantage here is that all of the collecting and correlating has been done for you. Carlita Boyles, creator of this program, spent years doing what I suggest in #1 – going through all sorts of textbooks and compiling lists of what kids need to learn to be ready for Algebra. In fact (spoiler alert) Math on the Level hits all of the points mentioned above about the three basic things you need in order to strike out textbook-free. Plus, the big advantage is that she takes the “grade level” piece out of the equation. Instead of thinking in terms of “third grade” you can think in terms of “fraction topics” or “measurement topics”.
Remember, however you compile your list, this is your road map, not your rule book. You’re free to use or discard anything you find. You don’t have to stick to the prescribed “grade level” for each topic. (You may notice as you look through various resources that there isn’t across-the-board agreement about scope and sequence anyway!) But if you’re nervous and want a framework to start with, begin with one or some of the above ideas.
The “Family” in “Family Math”
So, now you have a list of topics you’d like to cover. But how does this wind up being any different than the textbook approach when you have multiple students at multiple levels? That’s what I wondered, too, until I came across Math on the Level. (Truth in advertising: What you’re about to read is basically what I learned from the philosophy and approach of that program. Is it possible to have a crush on a curriculum?)
Not all students are ready to multiply mixed numbers. But all students are ready to talk about fractions. I promise you, even your Kindergartner knows what “half” is (or can quickly understand with a little cookie-sharing demonstration)! When you zoom out and think big picture, you begin to realize that everyone can engage together in exploration of the broad topics.
I wrote a guest post for the HEAV Blog about how you only really need to teach four things in math this year. Four things. Does that sound manageable? What if you took your whole school year and divided it into four quarters and took a quarter each to explore:
- Money and Decimals
- Geometry and Measurement
Pick a topic. Talk about it. Stretch it a little further for the older ones. Let the younger ones absorb as much as they are ready to catch and let the rest go for another day. You’ll hit it again many times!
How to Teach It
So where do you go for the information and guidance you’ll need on how to teach these topics?
Here are some suggestions.
- “Loving Living Math”. Think of this as a primer on Family Math. It’s a tremendous resource in a small package. You could read through it in an evening or two, and yet, it’s something you’ll want to reference again and again as author Cindy West gives great suggestions and resource lists for how to explore math in everyday life. (Hint: Learning math in “real life” means that it’s far more natural to include a wide range of kiddos than when, say, going over a math worksheet.)
- Your old textbook(s) or series. If you still have math textbooks on hand, you can probably find a little introduction to the concept at the beginning of the lesson covering that topic. It may be a little cumbersome to depend on this, however, as one grade-level book may not address the breadth of topics you’ll want to cover under one big idea.
- Read a book about it. Many of the early-grade arithmetic concepts can be covered by reading a children’s book illustrating the topic, like …
– Jerry Pallotta’s Candy Math Books
– Brian Cleary’s Math is CATegorical
– Stuart Murphey’s Mathstart Series
– Cindy Neuschwander’s Sir Cumferences Books
- YouTube. If there’s a math topic you’d like to explore and don’t know how to approach it on your own, try YouTube. There are tons of channels that address and explore math concepts. We love Math Antics. And of course, all of the Khan Academy instructional videos are available there as well. These are only two of many options.
- CTC Math. This is an online program that we’ve used in addition to Khan Academy. It provides helpful instructional videos/lesson for each topic. No reason why you couldn’t pull up a video from a child’s account (or your parent account) and watch and discuss together.
- Math on the Level. I’m sure you’re not surprised to see this one listed here. Included in this curriculum are four spiral-bound books – one each for the four “big topics” you’ll want to address in math each year. For each skill under the “big topic” Carlita has included ideas about how to teach it, including diagrams and examples. It’s all right there. There are also two supplemental books called “Math Adventures” and “Math Resources” which share ideas for math in real life, and extra resources like charts and graphs, and learning tips. You can look at some free samples of all six books.
To What Extent Have They Mastered It?
You know what you’re going to teach, you have some tools in place to help you teach it. And you’re ready to try teaching everyone whole-group. So, now you just need some way(s) to measure how much they understand, and to differentiate practice to everyone’s individual mastery level. Here are some ideas.
- Talk about it. Yep. That’s right. Explore a concept and then talk about what you just learned. You already naturally do this with other topics. You don’t feel compelled to have your kids complete a written assessment on every single thing you read together about literature, history or science, right? Math is a language. It is a way of communicating ideas. That communication can be done verbally as well as in written form, just as with any other subject.
- Games. For most any concept you want to practice or assess, there’s a game for that. You can check out this list of some of our favorite board games. Find printable review games on place value and fractions here in our shop. Check out the tons of games created by Math Geek Mama, Bethany Lake. Purchase or check out some of these resource books:
– Addition Facts that Stick
– Subtraction Facts that Stick
– Games for Math
– Math Games for Number and Operations and Algebraic Thinking
- Whiteboard. If you do want them to try some written practice, let them use the modern-day version of “slates”: a whiteboard! This could be a personal-sized one (we actually use laminated card stock paper on a clipboard or even the drawing app on our tablets) or a bigger one on the wall. Give a sample problem. See if they can solve it. You don’t need twenty examples to check for understanding.
- Paper or worksheet. If you still have your old math books, you can always pull or assign a few problems from that resource. Or just jot a few exercises on a piece of notebook paper. (If you like paper-pencil work, but hunting down example problems for each concept seems like too much work, you’re going to love #5.)
- Math on the Level. You knew this had to be in the list, right? Math on the Level comes with an excellent “Overview and Record Keeping” binder full of everything you’ll need to track which concepts each student has mastered and practiced.Instructions are included for developing 5-A-Day sheets for each student: five problems a day to continually review previously-mastered concepts. Each of the four “big topic” books for this curriculum includes an appendix with practice problems (and answers) for every concept covered in the book. Even more exciting is the brand new 5-A-Day Online Essentials. If you’d rather not keep records or write up Five-A-Day problems by hand, you’ll love this system. Using the custom-created spreadsheet, you can track student progress and then, with a simple copy-and-paste, transfer data to the Online Essentials program, which will automatically generate a printable practice sheet! (Note: You can make use of the Online Essentials whether or not you are using the full Math on the Level curriculum.)
- Online practice and games. This is our current go-to strategy at the moment. Not every family is a techie-family like ours. And not every family has access to enough screens to make this option workable (each of my four oldest have their own Chromebooks and the oldest six each have Kindle Fire tablets). But if this is your style, you can explore concepts whole-group, and then assign everyone online practice at their own level. (Stay tuned for more resources on this angle!)
As you read (or skim) through this post, I really hope that you take away three important thoughts:
- You don’t have to have a textbook or divide kids into grade-levels for math instruction.
- You can do this. There are tons of resources available to support you (see above).
- There are so many different approaches that you can tailor it to the needs and family culture of your homeschool!