The answer is no… one reason is because children are very different in how they learn math best once they are generally leaving the hands-on learning stage aside.
Some children still really thrive with hands-on math and might not learn well unless some types of manipulatives remain often in the lessons. So keep using manipulatives if this is what makes math really enjoyable for them!
Some prefer the “hands-on” application of math to be in with science (i.e. physics) instead and want a workbook or textbook for regular math lessons and practice.
Tip: Try to do math outdoors some of the time and also apply math to real life projects (e.g. building a sandbox, etc.). Outdoors is great for anyone but I think it is of extra-special interest for kids/teens who really like hands-on learning in math!
Some families want to prepare a student for upper levels by using a spiral method.
Some families want to prepare a student for upper levels by using a mastery approach.
Some families just want a very basic understanding of math which is then applied to real life in experiences.
Some families like a newer style or multi-media or something taught with a different methodology for setting up a problem and then finding its solution.
Some families (like ours) prefer to keep things in unit chunks similar to the “old math” taught in Canada in our generation and previous ones, preparing a student for both a real life math application as well as abilities to succeed in post-secondary coursework in math. (See here for “high school“ ideas.)
Some families will prefer an “old-fashioned used” textbook (e.g. from grandma’s day), others a worktext, others a newer textbook, etc..
We prefer something with paper in our family for math and we wanted something that was Canadian with the metric system with degrees Celsius, Canadian-based place and people names rather than American word problems, etc.. (It’s harder to input symbols in a computer but it has been done in upper levels too.)
Once the foundations for math have been laid in the early grades, it really depends on personal preference as to which direction and approach fits YOUR family the best!
One way to arrange junior and senior levels of math is to try to cover similar math sub-topics on some days. I have a printable chart for how I at least organize math resources in our family for elementary levels in another post (click here for that post).
Math Curriculum Our Family Has Liked
We used to distribute Math Mammoth curriculum for the grade 5-8 levels; it was excellent for being comprehensive and generally laid out in a unit-chunk style as well. It has its own style and methodology that we liked in many ways.
However, we did not personally like it before a grade 5 level, partly due to fairly small print for the younger grades and partly because I wanted more hands-on and visuals for K-2/3. The print size is good though for grades 5-8.
The other frustration we have found is in the “Algebra 1” title which used to be considered a pre-algebra/early algebra for grade 8 kids who like math. Some of the pages are good to use but some pages go far beyond an introduction to algebra for example, covering topics more in-depth or introducing them before public education standards in Canada would. Thus, if using the “workbook after grade 7”, you might need to preview and un-assign pages. (For example, there are pages within it which Canadians might think are for grade 10-11.) Note: If we use Math Mammoth in our family, we’ve used the “Golden” version because we wanted to have fewer lesson explanations to read and also wanted the freedom to teach a method for solving which we liked but perhaps would not be used in the curriculum.
There IS an answer key and all the workpages are hand-crafted, carefully thought-out by a mom who loves math education rather than a computer-generated bunch of practice questions. Also, the skills covered are not just “basics” or “operations”. The program includes graphing, geometry, etc.. These features are welcomed for upper-level math curriculum! (Disclaimer: While this author’s math program is good, we do not promote her religious studies.)
For a while, we offered Prism Math for grades 3-8. They are also very good but they are now out of print which means that quantities are limited to whatever suppliers have left. (We have none left. Amazon or Chapters/Indigo might still have a few.)
These are CANADIAN MATH consumable worktexts, one per level. They are classified as “colours” rather than grade levels.
(An aside – We did not carry the brown or gold levels (Grades 1-2) since I did not think they were as age-appropriate as the red to purple levels (Grades 3-8). They didn’t have enough hands-on or visual elements to them for young primaries in my opinion. Today, our family is very happy using our PSLC’s Math Sticks for K-2 instead!)
Back to writing about Prism Math series…
Although they were promoted as resources for “struggling students” who could not read at that same grade level, to me, “reading complex sentence structures with rich vocabulary” is not a necessary factor in one’s ability to succeed in math. To me, when I teach math skills, my purpose is to teach math. When I teach reading skills, then I’ll be concerned about complex sentence structures. But not in math class, as long as a student can understand ordinary sentences and instructions and compute what is right and logical.
If you can find them…what are the books like?
The math concepts are well organized into units (chapters). Concepts sequentially increase in difficulty as the students gain practice and confidence in how to perform the math required to solve the problems. Print is large and there is a good amount of white space to complete the work on the page. (Alternatively, we have used it like a textbook with the student writing in a lined notebook.)
The word problems are generally about very sensible situations and use names and places relevant to Canadian students.
Generally on one side of a lesson page you would find computing-type of questions (those are the kind with just numbers to work with) and on the reverse side of the page, you would find word problems to apply those same math skills. This is the way I think all math curriculum should be like ideally, once you reach around that grade 3/4 level! This is the time when “real life” application of math generally lays aside the hands-on manipulatives and picks up more word problems.
The chapters include all math strands (including operations, geometry, graphing, etc.). Each chapter begins with a simple pretest (to review past year’s skills), then the lessons, then a practice test in summary of what was learned. At the back of each book there are cumulative review tests for each chapter, a mid-term test for chapters 1-6 and a final test for chapters 1-13.
Like many programs developed for “struggling readers”, just pick and choose how many practice questions are beneficial for the student and un-assign the rest.
The main downside of this series is that there are NO ANSWER KEYS. The way we can overcome this inconvenience is to look on the bright side and remember that we, as parents, are teachers who have passed grade 8 math before. Old-fashioned teachers used to both make up the tests and the answer keys in years past so this isn’t beyond our capabilities. The tests are short and some of them are multiple choice. The tests are also straightforward in language structure since this series isn’t out to trick anyone or cause extra confusion – they simply want to teach students math skills in a solid manner. So, as parents, we can do these short tests ourselves and make up our own answer key. (We personally don’t choose to mark the lesson work since any major issues with grasping a skill will either be noticed by the student and he/she will come over for help or else it will be noticed in a test to be retaught then.)
We used Jump Math once in grade 3. It was a fairly good program at that time, especially for fractions.
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)
These are math resources which we have not used ourselves. However, they looked interesting-enough to mention in this blog.
Vintage Resource – Ray’s Arithmetic
A friend of mine mentioned this one to me recently. It has similarities to some of the vintage math readers and math “textbooks” I have in my small collection from the years my parents and aunt taught in Ontario rural schoolhouses (or attended them). (I’ve used these to supplement something a bit but not exclusively or extensively.) Perhaps if I was closer to the beginning of homeschooling and had more time/energy, I would look into vintage math more.
Ray’s Arithmetic is an all-grades type of resource which might be of interest to homeschooling families looking for something that has a strong mental math component and want to be very involved with teaching math. (I would not suggest it for those who are only temporarily homeschooling for a year or two though.)
To download it (at someone else’s website, not ours), click on the bolded name (above). You can also preview what it looks like here.
More thoughts about using something made for “strugglers”…
If a product appears that it is intended for “remedial students” and you know your student is an average or even a gifted student, this might actually be an excellent product for you to consider anyways! Sometimes, things get marketed sort of funny in my opinion!
So how you can tell if something is below-math level or at the right math-level? Do it by simply comparing the skills expected in a resource with the expectations in the ministry of education standards in your province/territory/state (which can be found easily online) or sometimes by comparing a detailed table of contents of two resources, one being marketed as “at the average or better level” and the other “at a remedial level”.
See if there is really much of a difference in the math part or is it just how many trivia puzzlers are added. You can always add puzzlers if your student really likes these. What you really want is to be assured that your students will be presented with an excellent level of math in the curriculum resource(s) that are chosen so that they don’t “fall behind” in this subject.
I’d like to explain this a bit further…
There are some students who enjoy challenges and puzzlers of all kinds, who like overcoming tricky questions that are worded on purpose to confuse/stimulate and get a brain really digging for advanced logic. And there are students who enjoy knowing “why” something works in math and to prove the theories behind why it works the way it does.
But I don’t believe these students represent all or even most average/smart students and thus, I tend to stay away from curriculum which focuses on theories or tricky questions meant to challenge students. The theories and tricky questions could even be the reason why there are many students and parents who claim they don’t like math! (I don’t know, but I wonder.)
IF a student likes these sorts of things, there are plenty of puzzlers and challenges that can supplement a math curriculum and that means, the rest of the students don’t have to feel frustrated or discouraged over something that really isn’t all that important in gaining the ability to do both basic and advanced math calculations and logic well.
I was a pretty good student in math, even taking it a wee bit of it in university (because I was a science student), but I personally don’t care about the theory or “whys” in this subject – I just want to know the “whats”, “whens”, and “hows” and apply things (e.g. like a pattern) to make it work correctly. Call it personality or preferences or whatever – but this is how many people view the subject of math, including our oldest who excelled in advanced functions and calculus.
(Some people call this “procedural” methodology for learning math. I mention it more in the post about high school math.)
When a curriculum presents itself as “for struggling students” but all it really is is a method of just being straightforward (which is what math should be for elementary levels), then I get a little perturbed.
To me, a “struggling math student” should define someone who fails to grasp much of the math skills and needs extra help to work with numbers or lines. It has nothing to do with not preferring to know the theories behind something or comprehending complex word-sentence structures. Test complex reading comprehension in reading and leave the math complexities to math stuff. Please don’t call people who don’t enjoy that unnecessary sideline of math “struggling” if they can work well with numbers and apply math to real life! They’re really not struggling with math – they just don’t appreciate the theory or quirky puzzler sidelines of it.
And quite possibly they also aren’t struggling with “reading levels” either. I know I wasn’t – I was an early reader and top student in reading comprehension. But if you put poorly-worded or super-complex sentences in math, then I (or other students I know) can get confused and even sometimes fail. Yet if it is worded more clearly, we can do the math correctly most of the time.
For high school, especially after grade 9, the topics tend to change or especially emphasize certain parts of math concepts, depending on whether or not the student is “struggling” or “gifted” or “average” in understanding math up to that point. THEN, I think it IS a good idea to match curriculum with individual strengths/weaknesses because the content covered in the various options likely will not have as much similarities as the elementary levels have had. In other words, consider remedial or practical-focused curriculum for students who aren’t expecting to take math or science at a university-level. But that is about the high school levels. See this post here for those suggestions.
I believe that math should be presented in a straightforward manner for all elementary levels (and even beyond that in some cases) because this is the period of time when students are learning the foundational skills and these need to be very solid for future success.
Perhaps it is time for a change in your math curriculum. We know from personal experience that methods can make a huge difference in whether or not a student grasps math concepts well! And sometimes, we’ve had to make the changes to a different curriculum, one that isn’t out to see if you can catch the tricks in every question and one that isn’t poorly-worded.
Recycling resources in a blue box can be a good thing!
I don’t think that math should be overly frustrating in elementary years for anyone. Start with what students already know, add to the lessons in a clear presentation to show “how”, subtract the distracting aspects, and give it some time to show itself measurably useful in life.
Keep up the good work!