What might be good options for homeschool math during the high school years? What has our family appreciated for learning math in the teen years? And what else might we consider sometime?
(When is it good to try out a new curriculum for math for high school? I think that whatever is working for a student for Algebra 1 should be also used for Algebra 2 to keep those consistent. The “best time” to change would be either around the pre-algebra stage or after algebra 2. For one of our students, we even had to switch in grade 12 because the curriculum just was not meeting what she needed to learn well. So a change can be indeed very beneficial, even if it’s late in secondary education, and result in good success!)
Nelson Textbooks (Canadian)
For the high school levels (after trying or looking at a few types of typical math curriculum), we first settled for a number of years with Nelson textbooks from Nelson Education (Canada). We’ve sometimes sold these textbooks as well, as special orders, but no longer do so.
Yes, they DO provide answers in the back for the questions in the textbook. (These answers are not “solutions”, meaning that the answers are not written out as step-by-step how to reach that answer – they are only the final answer. In contrast, a “solution book” which shows the steps involved is often limited to classroom teachers and is quite expensive as well.)
Nelson textbooks contain lessons with examples, problems/exercises to solve, answer key including for the chapter self-tests, which we use as “the tests”. We’ve had teens who do fairly well in math if it is presented clearly enough. In comparison to traditional homeschool options, we felt this series was one of the clearest in its presentation.
However, we continued to keep our eyes open for a program that might be easier for homeschool purposes, clearer and more concise.
We also wanted something that was not overly “American” in its tone for word problems or applications. Also, sometimes, the American methods for upper-level math are not the same as a Canadian method that we ourselves have learned when we were in school. (My husband has a math minor on his business degree and did very well in high school math in Ontario. So when he looked at various curriculum options, he noticed some differences. One of our teens who did well in a few advanced math courses at a local high school or with Nelson texts in general, also noticed differences to the extent of doing very poorly with understanding a popular USA homeschool curriculum so she changed back and was fine.)
The titles we have personally used with one or more of our family are: Principles of Math 9, Principles of Math 10, Functions and Applications 11 (this is the college/university pathway one with less theory emphasized but same math skills from what we can tell as the Functions 11 university pathway one), Advanced Functions 12, and Calculus and Vectors (grade 12).
We have also seen Mathematics for Everyday Life (grade 11 & grade 12 levels – intended for workplace students, not those heading to post-secondary) and can recommend those as well.
Update June 2021: For families wanting lessons taught, there ARE now Youtube channels which have high school math teachers teaching the lesson material according to these textbooks. So it’s like having a video component plus textbook. (At times though, the videos can be poorly organized/labelled as to same sequence/order of lessons as the textbook.)
Nelson textbooks would be our pick for “textbooks” in many ways. But for practical factors of marking, we decided our family would do better with something else, at least for now.
Nelson Handbooks (Canadian)
We also have appreciated the math handbooks of the following (and may have some copies still in stock):
- 0-17-620342-7 – Math to Learn (Canadian version for grades 1-2)
- 0-17-620344-3 – Math to Know (Canadian version for grades 3-4)
- 0-17-620340-0 – Math at Hand (Canadian version for grades 5-6)
- 0-17-620346-X – Math on Call (Canadian version for grades 7-8)
- 0-669-47151-8 – Algebra to Go (high school level handbook)
- 0-669-48129-7 – Geometry to Go (high school level handbook)
We are currently using an online math program, for the high school years only. (We do not intend to use CTC for elementary levels though since we do not want online studies for that age. We try to limit screen-time in our home overall.)
This is mainly due to Rob (homeschool dad) being available less for marking high school math. I never really did that level of marking since my time is more needed with younger students and household tasks. (We are fine with marking the elementary levels of math tests in our other curriculum choices though.) Our older daughters have helped with occasional math questions from teen siblings but we wanted a math program that would take these responsibilities more than what the Nelson textbooks could provide.
So we changed to CTC, essentially for four reasons:
- All math is marked by CTC, not us. (Evaluations are very easy to average for grade reports.)
- The video component is short and straightforward. We didn’t want long math lessons. (CTC does not seem to focus on a lot of theories.)
- The math work portion is specifically to be printed on PAPER, done on PAPER (e.g. away from a screen), and then submitted on the computer through the use of matching letters of answers.
- The application/scenarios of “real life math” are mostly applicable to any student in any English-speaking country. (The program itself was designed in Australia.)
The downside we see in CTC’s grade 11 is that the number of lessons are more than what we feel are necessary, so we would like to see them combine more and/or require less review/repetition of past lessons. With students possibly working for summer jobs by this stage, it can be discouraging to “still have 16 more math lessons to complete” at the end of a school year. It is my understanding that their team is considering comments we provided them for improvement.
Overall, we think CTC is a good option and plan to continue it using it for one of our teens.
Pre-University Math Courses
Check your province’s university course offerings to see if a “pre-university course” (which does NOT count for degree credit) for math, equivalent to what is deemed necessary by that school to enter a degree program, is available to take in-class or online. This is what one of our teens did to finish the “grade 12 math”.
This means that there is a professor/instructor with tutorial help, instead of working through a textbook by oneself. It also means that the coursework is narrowed down to the skills and concepts which make more sense to know.
(The cost may be higher but for some students, this is a very good option.)
These are math resources, most of which we have not used ourselves. However, they looked interesting-enough to mention in this blog.
Key to Algebra
This title is the most advanced group of workbooks for this series. From my understanding, it approximately covers what the Canadian public education system considers grade 9 math and perhaps a wee bit of grade 10 (depending on which grade teaches quadratics).
We plan to use Key to Algebra with our grade 9’er next year. Even though we study geometry and measurement each year so he already has the grade 8 level of those topics, I plan to also use those booklets (of Key to Geometry and Key to Metric Measurement). I want to do those booklets together as a multi-grade group with his younger siblings but I will include him because I don’t want to leave geometry and measurement “out” of grade 9.
(If he completes Key to Algebra and has significant time leftover (which he might because he is a “quick learner”), then I think we’ll add some review with the later LightUnits from Algebra 1, Christian Light Publishers, for the remainder of the school year.)
I appreciate the larger print (which would be helpful to one of his younger siblings who has a vision challenge), simple instructions, and non-distracting look to the Key to Algebra. While I looked at a variety of online reviews and remembered that a friend years ago really liked this series for her homeschooling family, I really liked how this YouTube review showed this series of consumable booklets:
Math Without Borders
This math program apparently teaches by providing full step-by-step solutions for about half of the assigned questions in a textbook (using video-based learning). In other words, the student work is “taken up in class” so that they can see “where” they may have missed something. (You can search for that program online if it interests you.)
The Grand Math Connection (Alberta)
This one is from Alberta (Canada) and based on that province’s standards/outcome. It is website with math courses developed by a grandfather (retired teacher) and his grandson. I liked the size of print and straightforwardness of the lessons when I looked at it briefly (Grades 10-12 levels). There are videos and printables. Their website is https://mathpqjq.com/ .
While Math-U-See was not a good fit for our family for elementary (we didn’t like how the lessons were arranged), it was on our “short-list” of possibilities to try for senior high school. We considered switching after “Algebra 2” for one of our teens – so it would just have been for the tail-end of their series. There is a Canadian distributor for this program in Western Canada who often advertises at conferences in the spring.
Christian Light Education, Rod & Staff Publishers
Being a publisher/distributor of curriculum for resources useful to a Mennonite-perspective education, these companies have done fairly well in the area of training with practical, real life math for trades and home businesses.
Additionally, CLE (not an affiliate link) is in the process of developing resources for math courses which look to me like they could be a good option for students intending to go onto post-secondary degree studies (i.e. more academic math compared to what many homeschoolers in the past would think of CLE offering).
I have seen sample pages of CLE’s Algebra 1 and like parts of those. Algebra II is to be available in June 2023. I like the layout of the textbook and also the feature that there is a solutions manual available, not just an answer key. (With a solutions manual, a student could mark his/her own daily work or check it first instead of asking for a parent/older sibling’s help.)
The downside is that there looks to be more-than-sufficient review-type questions in each lesson. (The term for this approach of continual review is “spiral”. See below.) But I like that the focus is on “how” (procedural) rather than “why” (conceptual) and this method is hard-to-find in upper-level math these days.
CLE remains on our “short list” of possible future choices to try, especially for someone who likes history and physics (which have themes in Algebra 1).
Recordkeeping (Rod and Staff Publishers Inc.) – One of our sons took part of this course and enjoyed it. It is a longer-than-average course (so he ran out of time to complete it). But he felt that it was very good in how much it covered and how it was arranged. He’ll use it as a reference guide likely.
There are other math-related courses which could be considered during the high school years as well. Our oldest daughter enjoyed a drafting course we found years ago from a school in British Columbia (which is no longer available).
Spiral or Mastery or Chapter Chunks?
The Spiral Approach
The spiral approach is perhaps the most common in the curriculum market of homeschool math. Saxon, ABeka math, Singapore math, and many other companies produce this kind of math lessons. The basic idea is that, to learn math well, one must have constant review of past understandings and learn new stuff in tiny increments. The key word is constant. This means that most or all lessons have a review section in the lesson to complete and all new concepts are introduced very very gradually.
For some students, a constant review might be helpful or even enjoyed. For other students, the constant review is a distraction to vie for attention away from what was just learned in the new portion of the lesson, truly annoying, and can seem like a waste of time to even bother trying to like math.
For students who like to grasp a single concept in a shorter period of time than multi-lessons, the spiral approach can also add frustration since it might not present enough of the skill’s concept(s) in just one lesson. Spreading out, say, over a week or more, the math steps that a student might find useful to know about sooner than later, can hold back a quick learner. It can also confuse the kind of student who learns best by seeing “the big picture” first.
Our family has never done as well with a spiral-type method. (This includes us as parents. We learned to “cope”, at least for some math.)
The Mastery Approach
The mastery approach has also been prevalent in the homeschool math market. Math-U-See is perhaps the most well-known company. In elementary levels, their mastery approach even shows on the title of the curriculum for which main skill is focused on for the entire grade/level of math! Math Mammoth has somewhat a mastery approach but to less of a degree; it seems to teach a greater variety of topics within a level. (But then, by the end of that program (e.g. Algebra 1), it looks like it is less mastery and more little steps with more review, alongside the challenge questions at the bottom of the pages.)
For students who like to focus on a single skill or single set of skills for these upper-levels, at least until it’s solid and can be combined into more complexity, mastery looks like a better fit. However, what happens if the students want a broader variety of skills in that same year/grade/level? This is where mastery can become boring and dull. And this is where I think the mastery approach gets its real downside.
When I was a student, the grade 9, 10, and 11 classes were taught things in neither spiral or mastery in the sense of what I just described above, at least not according to my memory. I think students back then were also less frustrated and more able to understand and use math.
The “Chapter Chunks” Approach
Now I really don’t know if there is a better name than “chapter chunks”. But all it really means is neither the extreme of spiral nor mastery. It goes like this:
The students get a lesson on a skill, including a general “where are we going with this” in the same lesson. They see a few problems modelled for them. They try easier, then harder problems related to this day’s lesson. Generally, they don’t review other skills unless those are used within the easier/harder problems of that specific lesson. (That is, they don’t review until perhaps a review-type day a few weeks later. Then that day is for review, not a day for learning new skills.)
The skills are organized into chapters. These aren’t just chapters dividing how much time it takes to go through a math course. Rather, these chapters relate to similar-types of skills, grouped together in a logical, common sense sort of sequence.
How about a chapter where algebra applies to measurement, for example? Another one about solving equations algebraically. Another chapter or more relating to geometric shapes. Another one where concepts apply to graphing. And every once in a while, some cumulative review lesson days appear as a reminder.
Each grade level increases in depth on each skill. (For example, geometry was something we studied as part of every grade, not just in grade 11.)
I realize, this is not the “new math” recommendations from the “experts” nowadays. But I think this desire to have a math program in high school which isn’t spiral or mastery is why our family has ended up trying various programs to see which ones have the fewer issues to cope with. And I’m sure we’re not the only ones.
Procedural or Conceptual?
These two words describe how the math lessons tend to be taught in a curriculum or program, in other words, the methods the author or teacher uses.
The most common methodology for math nowadays is “conceptual”. This means that students are taught “why” a math skill works, theories, proofs, and so forth. The concept of conceptual learning is that students will grasp math better if they understand “why” (and perhaps even discover or develop more concepts if they understand “why”). Then they don’t need to memorize patterns or write out steps to follow as much.
This is typically in philosophical opposition to teaching math using a “procedural” methodology. Procedural means that students are taught “how” to do a math skill, not always “why”. Instead, it works by memorizing a set of facts or steps which work. Based on trusting those truths, students solve math problems. They might see a pattern to follow and repeat as an example.
Sometimes the disagreement over which method is “best” for teaching math gets to a point of implying that “smart” students like/love conceptual learning the most and if you want to produce a “smart kid” in math, then stay away from procedural methods. I’d disagree!
To me, there is nothing wrong or inferior with procedural methodology of math. Furthermore, some of us “smart” (a.k.a. “gifted academically”) people actually don’t care about the “why” or the “theories”. We simply want to do our math well and move ahead. We recognize that the “why” truly fascinates some math/science brains but that some of us math/science brains are more fascinated about the “how”.
Either method should be fine to use, depending on the student.
The downside is that there is not an abundance of homeschool math curriculum for “on-level”-to-“gifted” students these days which isn’t emphasizing “conceptual” learning, especially for the upper-levels. (CLE apparently is more “procedural”. But it is also spiral with much review within each lesson. CTC Online Math is considered procedural.)
So for those of us homeschoolers who would like procedural methods in a chapter chunk approach, this can be like hunting for a needle in a haystack!