Alright, this should truly be the final sneak peek for this guide... until the BIG sneak peek coming for those on our email list.
I realized that I have not clearly laid out our math plans for Missions to Modern Marvels, so I want to do that in this post. However, to give you a bit of background as to how we arrived at these math recommendations, I will share my own background on the important, and often stress-causing
, area of math! Since I spent over a decade in the classroom as a public school teacher, and now have spent more than a decade as a homeschool teacher, I have had the opportunity to use (or preview extensively) many of the name brand publishers that are out there for math. Through over 23 years of teaching math to all different-aged kiddos, I have gradually come to the philosophy of math teaching that I now have.
I'm going to share much of this philosophy with you below, in the hopes that it may make you ponder your own philosophy on mathematics instruction. Your philosophy will often drive the decision you'll make about which math program to use, so I encourage you that it is worth spending a bit of time thinking about this important area! Also, be prepared that your philosophy will likely be a "work-in-progress" as you and your students mature, so don't be alarmed if you make some shifts in your thinking before you're done! With that in mind, here is my philosophy at this point in time: I believe that kiddos benefit from hands-on, manipulative-based activities in the pre-K through grade 2 years. I think some students need manipulatives more than others but that all students can benefit from them in the early years.
I also feel that manipulative use can go on too long and that there comes a time when students need to move from manipulatives to more pictorial representations (and later from pictorial representations to more abstract thinking). I feel that math fact memorization is important but that we tend to push it upon our children before they realize the need for it (and often before they can understand what the facts actually mean). Thus, I have grown to appreciate waiting longer for students to gradually memorize their facts on their own, before stepping in with forced memorization of any remaining facts.
I find this to be true in both addition and multiplication fact memorization and have found that many students' initial dislike or frustration with math comes from forced fact memorization at too young of an age. I do think that memorization of facts is important, but if you are using a solid math program with incremental learning, the student should be given every opportunity to first internalize the facts on his/her own. It's also important not to equate fact memorization with math aptitude or understanding, as memorization and mathematical reasoning are two different things. Next, while the area of mathematics encompasses a set body of skills to be learned, mathematical reasoning does not always come along with the teaching of the skills. What I mean is that a child can learn and memorize the "steps" to solve certain types of problems without ever comprehending why he/she is doing these steps. Programs that emphasize teaching the steps for problem-solving, before having the child grapple with how to solve the problem to "discover" which steps are needed, take the "thinking" out of the equation. This is the reason that the "why" behind the "how" has become critically important to me in the teaching of math. Otherwise, math just becomes a set of steps to memorize, and when the sequence of steps cannot be recalled the process of solving real math problems breaks down.
I believe that solving math problems in one's mind is a skill that has to be taught, practiced, and developed; much like any other thinking skill. For some students this skill comes more easily than others, but for most students learning "how" to solve computational problems in one's mind needs to be taught. It takes so much more to learn this skill than just "telling" the child to "do it in your head". It is important to actually show the child "how" you could "do it in your head" and then even more important to show the child "why" this method works!
I believe talking through math problems and discussing possible ways to arrive at a solution is an integral part of math. When students get "stuck", talking through the problem out loud can really help. Math should not be a silent subject. Mathematical discussions are key.
I think that the amount of math problems in many texts have expanded through the years, and continue to expand, simply to fill the 45-50 min. time slot alloted to math in most public school classrooms each day. This expansion of problems usually results in a "supersized" number of drill and practice type of problems, which must be taken into account whenever you are looking at using a math program written for the public or private school classroom at home.
While programs can be down-sized for home use, down-sizing takes time and daily decision-making as to what to skip and what to assign.
This is why I prefer fewer problems, at a higher level, instead of many problems that call mainly upon rote memorization or basic computation to solve. I am much more likely to sit with my child and help with math when there are fewer problems (that are more difficult), as I can see my time commitment will be profitable and reasonable! However, if there are too many math problems (many of which are drill and practice), I am more likely to walk away leaving my student to complete the problems on his/her own. Typically, then, I discover that my student only comes to me when he/she has reached the frustration point, which is not a positive moment! I believe that some students have a natural God-given aptitude toward math but that all students need a foundational level of math to function in today's world. For us to expect ALL students to attain the pre-calc, trignonmetry, and calculus level of math is not reasonable, nor is it necessary. So, balance among the subject areas becomes important along with time spent seeing each student's strengths and weaknesses as a necessary component of what that "balance" looks like.
I do think that grappling with higher level mathematical problems is something that is important for all students to do, as I think it teaches kiddos to stretch their minds as they work to solve the problems. However, it is important that students have the foundational level of mathematical skills needed in place to call upon as they attempt higher level problem-solving. So, if students have not mastered the foundational skills found in most 6th grade math texts, then it will be important to focus on those skill areas prior to proceeding to higher level maths such as Algebra I and II and Geometry.
Last, I will share that I believe that an extensive amount of math presentation is not necessary each day as that is a classroom-oriented approach to math. Rather, a short introduction to the day's concepts through either a bit of presentation or through talking through some textbook examples is sufficient prior to beginning to apply the day's learning. But, I do believe the parent should be present and engaged with the student as the student works through his/her math workbook lesson each day.
I have come to believe that math should not be a do-it-yourself subject (or the parent will quickly find himself/herself out of the loop as far as helping the child goes). This is why we never list math as an independent subject in our guide. I also believe that a full-text answer key is imperative to a parent's ability to help a child in math programs from Algebra on up. This is because line-by-line analysis can then take place using a full-text key, and this is so necessary in discovering where the child went wrong in solving the problem!
For all the reasons I've shared above, we have chosen Singapore Primary Math in the younger years and a choice between Singapore's Discovering Mathematics or Videotext Algebra in the upper years. Even if you don't completely agree with the philosophy I've shared above, please realize that does not mean that these math programs will not be a fit for you!
I simply share my philosophy about mathematics in order for you to understand why we have chosen the math programs that we offer with our guides.
There are many good, solid math programs available, and I do not pretend to think for a moment that everyone will use the programs we recommend. I do, however, want you to know that it is not without much thought that we arrived at our math choices and that my philosophy of mathematics is what drives my mathematical recommendations. So, it is hopefully worthwhile for you to read my thought process as you seek to define your own in this area! Blessings,
Carrie
Sometimes more is just more and really is not better.