Homeschool – Math
I love math as much as I love history! However, mathematics is often a much hated subject. So let’s see what we can do to make sure our children are comfortable with mathematics.
Choosing a Mathematics Curriculum
When deciding on math curricula for your children, there are two important concepts to understand. The first is spiral verses mastery curricula, and the second is procedural verses conceptual math. Let’s get into the differences between the two, and what they mean for your children.
Spiral VS Mastery
A math textbook that “spirals” concepts offers frequent opportunity to review what has been learned at early stages and to build upon that knowledge. So one week you may be studying adding numbers up to ten, and then next week you may be doing shapes, but the week after that you would go back to addition and perhaps work on adding numbers up to twenty.
Spiral programs are good for how often material is reviewed. Also, children who get bored easily and would like to change what concept they are working on frequently will enjoy a spiral program.
A mastery textbook will focus on one concept for a long time, working to build “mastery” of a subject. This type of program is good for children who would be frustrated by distractions, and who really like to understand what they are doing before moving on. However, because mastery programs work on a concept for a long time, there is often a long span between when a topic is finished and it will be reviewed again. If you are concerned about your child forgetting material over time, be sure to add opportunities to review earlier concepts throughout the year.
The Math with Confidence series recommended below is a mastery program that builds in spiral review to the daily workbook pages. The other programs I recommend are both spiral.
Making a spiral program work for mastery
However, if you want to spiral less and work on mastery for longer, I have a plan for that! Use the table of contents to see when addition comes up again and flip to there to continue on the same topic! This way I can use the excellent spiral programs, and still adapt it to a mastery approach if it seems it would benefit any of my children.
Conceptual and Procedural Math
Conceptual programs focus on teaching the grammar of math. That is, the concepts behind why mathematics work. Procedural programs focus on how to solve math problems – procedures for finding the answer. Here’s the thing: our children need to know why math works, and how to find the answer.
So when you choose a mathematics program, it is important to be aware of whether it is conceptual or procedural. If you choose a conceptual program, you know you are going to need to spend some extra time working on how to actually solve math problems. Use math flashcards, and math drills. A quick note – avoid timing the dills, the extra pressure helps no one build math confidence. Another option: a program for helping memorize math facts to supplement a conceptual program with procedural practice. I have been collecting books from the series Math Facts that Stick for this purpose.
If you choose a procedural program, you will need a conceptual supplement. Khan Academy videos offer a free visual supplement to procedural mathematics. Otherwise, Miquon Math is used for a more hands on supplemental approach.
Preschool Math
Although it is possible to do early academics with children, the main purpose of any pre-grade school math is to form a basis in mathematical thinking and vocabulary. A child who is surrounded my words like in addition, fewer, volume, area, and longer, will not be intimidated by math when introduced to equations and geometry later. Count stairs with your preschooler as you climb them. Add and subtract things from your grocery cart. Talk about things you measure, or the shape of objects you are using.
For a workbook free preschool math guide, check out Kate Snow’s Preschool Math at Home.
If you have a lot of time (for DIY) or have some disposable income, Montessori math materials are another good option for preschool mathematics. The MontessoriAlbum website has the step by step process for introducing various materials and mathematical concepts for ages 3-6. Personally, I spend all my birthday and Christmas money on the beautiful hands-on Montessori materials, and the girls get Montessori materials for their birthday and Christmas/St. Nicholas Day gifts.
Mathematics with Grades 1-6 Students
In the early years, mathematics nearly as important and learning reading and writing. Ideally math should be done every day of homeschool, and no break from math should last longer than two weeks.
Procedure
- Aim to do around 4 math lessons + worksheets a week
- Add in your supplement as your child becomes comfortable with what’s in the textbook. And when your child is struggling with a math concept, use the supplement to build your child’s understanding.
- If using a mastery program, review a few question from previous worksheets once a week or once every two weeks
- Do some real life math a few times a month. Play store, do some baking, measure things around your house! Activities like these not only make math fun, but also help your child see how math is used in real life.
- Bonus: Read some math picture books! Sir Cumference books are my favourite so far, but I will do an article later with more of my favourite math picture books!
My Top Three Math Programs
Most Cost Effective:
Kate Snow’s Math With Confidence Series (K-6) is the most cost effective math program I recommend. It has the added benefit of balancing procedural and conceptual explanations, so there’s no need for supplements to this program. Snow is also the author of the Math Facts that Stick program, which I mentioned earlier as a procedural supplement which aids in teaching the memorization of math facts.
Not only is this program cost effective, it has the bonus of teaching both conceptual and procedural mathematics. Daily lessons are short (my four year old likes to do about two lessons from the Kindergarten book a day, and the workbook keeps things short and simple. Also while it is a mastery program, it integrates spiral review. For kindergarten each lesson begins with a review warm up, and in grade one and up, a second workbook page for each day is used to review and practice earlier concepts.
Oh! And another bonus to this program is before each unit and chapter set there is an explanation of the math for parents. It explains why we are teaching these concepts, how we do it, and what we need for the week ahead. At the end of each unit there is a page reviewing what your child should have learned so far, ideas for extra practice if your child needs some.
Best Procedural:
Saxon Math offers very thoughtful step by step instructions for mathematics. A nice thing about the homeschool program is it’s tied to skill level, not grade. So Saxon 5/6 can be done in grade five or grade six. And a child who is slower to grasp mathematics will not feel behind.
A quick note, you don’t need to buy the manipulatives for K-3, you can use objects around your home instead. And there is no need to do it twice a day (to do second side of the worksheet – one side is enough). Saxon also offers a daily meeting book, but this too is an optional component.
*Note, this program is best suited for kids who either need a lot of extra help with math, or find math very intuitive. It is a very spiral program, and drills practice of math skills for mastery. One downside to this program is it jumps around topics a lot. So it is not suited to children who need help seeing how math topics are related without adapting the program. So although this is often considered the “golden standard” for homeschool math, this program may not be the golden program for your family.
Best Conceptual:
Singapore Math/Primary Mathematics. There are several editions of this program, the best tested of which are the US Edition (follows Singapore sequence with US coins/measurement units) and the Common Core edition (things edited to reflect US Common Core standards). These two programs are interchangeable and you can switch from one to the other anytime. This program would be good for children who show an inclination towards math and/or abstract thinking early.
New this year, is the Primary Mathematics 2022 Edition, which follows the US scope and sequence for mathematics. This edition would be better for children who need a slower introduction to mathematics. (Multiplication and division are not introduced in grade one with this program).
Mathematics with Grades 7-12 Students
By this point, mathematics becomes very abstract. Because math is becoming more abstract during these years, doing real life mathematics once a week for grades seven and eight can really help keep things in perspective. a
Have your child practice buying groceries, and planning an event including making and following a budget. Try letting your child make a timetable for a homeschool day or Saturday, budgeting time for activities, chores, and travel. Go over how to balance a checkbook with your child. Have your children calculate monthly and yearly interest on credit card debt, and the cost of a meal at a restaurant verses making it at home. These are valuable math life skills to work on now!
What happens after finishing Algebra II, or whatever the equivalent is for your child to meet state requirements? This depends on the child’s math interest and career path ideas. It is probably best to check what university requirements are to be sure to meet those. However, for child who struggled with math for years, it may be time to take a break. Consider doing a reading course in mathematics instead. Reading about math could spark fluency in a way textbooks have failed for years. Otherwise, a reading course provides a new way to look at this subject in order to broaden the child’s feelings.
The Byzantine Life
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