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Ladies,

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

Thank you , Carrie. We are only in PM 1B, but this is so helpful in thinking about Math in years to come. We have a long way to go, but I felt compelled to read this. You made some comments that caused me to re-evaluate the approach I am taking, even in Primary Math. Thank you for sharing your wisdom. You've taught me so much since I've come to HOD!

This might have been covered somewhere else, but I haven't really been reading too much about the upper guides yet

What math level do you have scheduled for what "years"? Like, which guide will they hit pre-algebra, algebra, geometry, etc?

The scheduled Singapore doesn't do a lot of review in HOD. So at what point do you do review work and how much is appropriate on a regular basis to keep the time down on a daily basis?

I would like to add 1 more point to Carrie's extensive thought -provoking list on math philosophy. And b/c we fell into every hole there is to fall into with one of our children , who is not " gifted" in math, and switched programs more times than I would like to admit, only to fall into the same hole again. I think this qualifies me to AMEN Carries list plus add, that w/o giving this thought to your selection in math, you will find the child's confidence level is destroyed, then it becomes an issue of not another curr. but building their confidence.
I am thankful that we have the opportunity now to restore that for our child and have found out she is not gifted as I mentioned, but she can do math: and for Carrie, who has paved the way for us and is willing to humbly share her insight and able to articulate it so well. Also we have another child to NOT make those same mistakes on.
I would exhort you to read again these insights, print them out, highlight them and have them before you when you make your math selections, and not to be guided by your convenience, which I see so many people doing.
Blessings on your journey
KK

Carrie,
Thank you for your labor of love. This is our fourth year doing HOD. We started the year you wrote Preparing and will go into M to M next year. We didn't do Singapore because I thought it would be too hard starting in the middle of the program. We did different programs, however we are doing Math Mammoth now because it is mastery instrad of spiral. So which of the two programs that you recommend would be a better fit for him. Math is not his best subject. He needs good explanation. He will be doing pre-algebra next year in the 8th grade.
Blessings,
Diane

Pam,

Thank you so much for your comments and encouraging words. I'm so glad that you found some things you could put into practice.

Blessings,
Carrie

Lora Beth,

Good question! Missions to Modern Marvels will include schedules for Singapore Primary Mathematics 6A/6B, Discovering Mathematics 1A/1B, Discovering Mathematics 2A/2B and the alternative option of using Videotext Modules A/B/C for those students who do not with to use the Discovering Mathematics series.

The plan is to offer both Disovering Mathematics and Videotext as options throughout high school, with two levels of each in each guide. So, for example in the geography guide, which will come after MTMM, we would include DM 2A/2B, DM 3A/3B, and Videotext Modules A/B/C or D/E/F. (2 levels of 2 different programs) Videotext is self-paced based on daily quiz results, so there will not be a schedule included for Videotext. However, 3 modules is typically a school year, and we will offer help as to what credit can be given depending on the modules completed.

Blessings,
Carrie

Annaz,

This is another really good question. One common misunderstanding about Singapore is the "lack of review" that is perceived to be a discrepancy in the program that needs to be remedied. I had this very misconception myself, until I went all the way through the Singapore Primary Mathematics series from Earlybird Kindergarten through 6B (which my second son is just finishing).

Singapore actually does have regular review woven within it's pages. It is just done differently from the way that other more traditional programs handle review. One of the hidden components in the Singapore program is that the review of concepts is wound within the story/word problem aspect of the program (and the word problems are a strength of Singapore's for this very reason). So, every time that a student has a series of word/story problems, they are reviewing previous concepts. For example, one story problem may ask the student to use multiplication, addition and money. Another problem may use decimals, fractions, and percents. The next problem may have an aspect of time along with using division. The next problem may have geometry in it and have the students using area and perimeter. Anyway, you get the idea. Since Singapore math usually has kiddos doing multiple steps in its word problems, it also has them using multiple functions and types of skills.

Even within the practice problems this is true. For example, in opening the 6B textbook to its first practice page, which is not technically a "review page", there are problems on dividing whole numbers into fractions, fractions into whole numbers, dividing fractions by fractions, listing how many one-sixths are in the whole number 3, finidng how many half hour periods are in 4 hours, finding how many bricks weighing 1/4 lb. each will equal a total weight of 3 lb., finding how many pieces of string 1/5 meter long can be cut from a 3 meter string, finding how many kilograms of beef 4/5 of 2 kg. is, and so on. So, on just this practice page, we have various types of division, but also work with fractions, time, weights in pounds and kilograms, and measurement in meters. This is what I mean when I say that Singapore actually does review quite regularly! It is just done in the context of solving real problems, rather than done as drill and practice through basic computational problems. It is a different, more integrated approach.

Then, there are also actual lessons titled "Review" that occur in the text at the end of each chapter or two (or sometimes three depending on the chapter concepts). These are extensive and very in-depth reviews. There are reviews in the workbooks and in the textbooks, and students are expected to do both. The amount and type of review problems increase in difficulty accordingly as a student goes up in the levels.

This is why we do not advocate adding "more" practice and review to Singapore math, as the review is already built in! We have never used any additional practice books or materials written to "add to" the Singapore math program with our own kiddos, as these add-ons were not a part of the original program's design. Our kiddos have done very well with the program "as is" and honestly could not test any higher on their standardized tests in math. So, we are happy with their progress. We've not found the need to add any additional review either, although I had wondered myself early on if this might be needed. I held off in adding to the program and have been very thankful I did (as I can be the queen of the add-ons...and was with my poor first child). Sometimes more is just more and really is not better.

Blessings,
Carrie

Diane,

With your son being in 8th grade, I would stay the course with what you are using for Pre-Algebra. I agree that a switch to Singapore this late in the game would be hard for him and also would not be a good move, as he is in the verge of Algebra. So, my advice would be for you to consider Videotext, when your son has had some pre-algebra and is ready to move into Algebra I. Videotext Module A does cover Pre-algebra concepts very well and is very meaty, however we found having a pre-algebra foundation prior to beginning Module A of Videotext with our oldest son to be very helpful.

I would not typically advise using Discovering Mathematics with a child who has not come up through Singapore's Primary Mathematics series. However, if you do desire to consider DM, you can give a placement test for DM1A/1B at the following link just to see whether this would be an appropriate option for your son. DM1A/1B is mainly pre-algebra (with some Algebra I and geometry included). DM 2A/2B is mainly Algebra I (with some geometry included). The placement test is a good indicator of readiness for DM. Link: http://www.singaporemath.com/Placement_Test_s/86.

A better description of DM can be found here in a previous post of mine. Link: viewtopic.php?f=6&t=7945

You'll have to scroll down to the bottom of the link above to find the placement tests for DM. Currently, only tests for DM1A/1B and 2A/2B are available. The DM series is also going into a bit of an update, and so I am assuming the placement test will change accordingly.

One thing to consider is that all students using Videotext Algebra must begin with Module A. So, if you think you may wish to use Videotext for Algebra, it would be good to begin with it as your first Algebra program. You cannot technically come into Videotext in the middle, as the concepts build upon one another and are integrated. So, all students must begin at Module A, even if they have had prior Algebra I coursework.

Another thing to ponder is that for all those families who aren't sure whether they will like DM math, or not, it is possible to do DM 1A/1B for pre-algebra (and then if it wasn't successful still make the switch to Videotext once they are ready to begin Algebra I). If, however, the DM works well, then they can continue on with DM 2A/2B for Algebra I. But, then they must plan to stay the course through DM 3A/3B for Algebra II (or switch to a different Algebra II program... but probably not switch to Videotext or the child would have to begin with Module A even if they have already completed Algebra I).

Videotext does have a separate geometry/trigonomety program, so at that point it would be possible to enter in to Videotext even if the child has used something else for Algebra I and II. Anyway, I just thought I would clarify those few areas, so families know when the best time is to make a switch in and out of these particular programs, if needed.

Blessings,
Carrie

I have 2 of my sons in Singapore Math. Oldest is in 4B and the next one is in 2B. My first son doesn't not have the natural giftedness in Math and my 2nd one does. I really needed to read this philosophy today, Carrie. I find myself getting so frustrated sometimes with my oldest instead of embracing the discussions. I had this idea that he should be able to grasp it all without my help. I am thankful to hear that math should not be an independent box. Thanks so much!

MeadowWay,

Thanks so much for your helpful, encouraging comments. You added much to the discussion, and I appreciate your taking time out of your busy schedule to share!

Blessings,
Carrie

Larissa,

I'm so glad that this discussion was helpful in some way with your Singapore journey!

Blessings,
Carrie