On Teaching Math: Part Five
Welcome to A Mother’s Thinking Love: Living Ideas, Lovingly Shared! In my last post I shared, based on my classroom experience, why I think communal, family-style math can work in the homeschool. Not only do I think it can “work”, I think it can be a source of shared joy and delight for your family. In today’s post, I want to discuss some practical ideas. I know it may seem far-fetched now, but I think it will make sense by the end of this post. Join me for: “On Teaching Math: Part Five”!
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LINK TO THE REST OF THE POSTS IN THE SERIES
But What Do I Teach?
Math curriculums generally fall into one of two categories: mastery or spiral. A mastery based curriculum spends a larger time on one concept. Although some review of past concepts is often built-in, the majority of the time is spent on one concept, like multiplication. A spiral based curriculum puts a larger emphasis on review. A smaller amount of time is spent with multiplication than in a mastery based curriculum. Spiral based curriculums will spiral back to, and build on, multiplication concepts, but new concepts, like measurement, might be introduced in between multiplication lessons. Often times in a spiral based curriculum, students spend a significant portion of each math lesson reviewing past math concepts in a systematic way.
In both approaches, mother-teachers in the homeschool don’t have to think about what comes next. The curriculum takes care of that. In the approach I am suggesting, it may seem like the mother-teacher is required to do a lot more work. But, I don’t think so. I think it just requires work in a different way. Instead of teaching multiple different math concepts to multiple different students at one time, the mother-teacher plans work for the family, or maybe a couple of form-groups within the family if necessary.
What Should Children Learn and When?
Textbooks give us the idea that all children should learn very specific math concepts at very specific times. They must progress through a specific list of standards at a specific pace. I have found that this is not true, or not always true at least. If you placed a problem from an Algebra ll textbook in front of your kindergartener, I would not expect a fruitful math lesson. But in the approach I am suggesting here, students are not hedged in to rigid pathways. I talked about this more in “On Teaching Math: Part Four”.
In my math classrooms, I took neither a mastery or a spiral approach. When it came to the mastery approach, I found that students would get bored by spending weeks on the same topic. Spending four weeks on multiplication, even with some review mixed in, was an absolute bore. I was bored teaching it, and students were bored doing it. Besides, students will catch on to the pattern. They will know that every word problem is likely to be a multiplication problem, and they will put math class on autopilot.
My approach leaned slightly more towards spiral but not explicitly. We did move from concept to concept at a faster pace, but I did not require systematic review. We naturally engaged in review in our lessons and I planned some, but I just never found the systematic approach to be necessary.
Make Up Your Mind
So, if I am not suggesting mastery or spiral, what am I suggesting? I am suggesting that you give your children a wide, generous math curriculum. Yes, I am drawing from Charlotte Mason’s philosophy here. We give students variety in other areas but not usually in math. I am suggesting that in the same week, students might work with all four operations, fractions, and maybe geometry or measurement too.
How can you do this in your homeschool? Well if you have a math curriculum, this is where it can come in handy. You can use it to pull problems from a variety of concepts. Again, this will only work with word problems. Find basic problems in multiplication, fractions, and measurement. Follow the method of introducing, giving time for solving, and discussion that I outlined in previous posts. See how it goes.
It may feel awkward at first. You may find it challenging to choose problems, but you will get there. Observation is your friend. At the end of each lesson, make notes about the overall discussion and the work of each child. This can help you find problems for the future. Also, you will be pleasantly surprised at the connections your children make when working with multiple math concepts in one week! Many of my former students discovered on their own that their knowledge of multiplication facts helped them with fractions or that addition facts helped them with subtraction.
What If I’m Not Ready for a Feast?
Maybe you aren’t ready for a feast, but you do want to add more discovery and delight into your math lessons. You can flip each student’s math lesson upside down. Give them the word problem, usually found at the end of the lesson, first and go from there. Again, go back and read my teaching process for this. The discussion part won’t likely be possible as a family but each child can narrate his/her work to you. These small changes alone will make a difference!
Whether you are trying to sit down to the feast or still considering it, you can add in some of these ideas:
Cooking
Building
Math games
These are a few ideas to add a wide variety to your math lessons. Of course, please don’t start cooking and call it a “Math Lesson”. Just cook and know that your children are learning. You can make some casual observations outloud as you work, and your children might do the same.
Another option is to use the first two Learn Math Fast books as spines to help guide your lessons overall.
What Do You Think?
I hope you have enjoyed “One Teaching Math: Part Five”! Are you ready to try to implement some family-style math? Maybe even for just one lesson a week? Do you have any ideas to add? Share in the comments below!
