Kindergarten Curriculum Choices: Math Edition

In a previous post, I droned on and on about our search for a science curriculum. Today, it's time to discuss math.

There are so many options for homeschool math curricula that I cannot possibly describe all of them—not even all of the most popular ones. I will, however, talk briefly about the main ones we considered before I tell you what we chose. First I’ll talk about the mastery curricula (those in which the goal is for the student to master a concept before moving on to the next concept); then I’ll talk about the spiral or incremental ones (those in which information is presented in very tiny pieces, with new topics introduced and reinforced or elaborated upon slowly over time, so that topics are mastered gradually and concurrently with each other).

MASTERY-BASED CURRICULA

Math-U-See

• Kindergarten through Calculus
• Primer (K) level would be $91; subsequent levels should be less expensive because the manipulatives set would not have to be purchased again—however, the cost of the curriculum itself goes up in subsequent levels, so the price only drops by around $20.
• Uses manipulatives, DVDs, and songs to teach concepts and aid in math fact memorization
• The scope and sequences is nonstandard, so standardized testing scores do not always reflect students’ learning—the student may not have been exposed to all “grade-appropriate” material but may have mastered “advanced” material that is not yet being tested.

I watched a series of videos that illustrate the way in which mathematical concepts are taught using this program, and I admit to having a light bulb moment or two as the videos showed me new ways of thinking about and understanding math (a subject in which I’ve never felt particularly confident). This program’s unique way of explaining concepts drew me to it, as did several reviews that said that less than confident teachers were able to use this program to learn along with their children and become much better at math than they’d ever been before. However, Jeff and I both had concerns about reviewers’ almost universal assertion that this curriculum is not as rigorous as other math curricula.

Singapore Math

• Currently, grades K-12 are offered, though it was announced recently that this company is discontinuing the courses above 8^th grade.
• It is difficult to determine the exact pricing of this program, as each level requires 2 textbooks, 2 workbooks, and 2 instructor’s guides, and there are a myriad of supplemental materials (advanced word problem workbooks, review workbooks, etc) that some users find critical and others find unnecessary. The consensus among members of homeschool forums tends to be that this is one of the most, if not the most, expensive math curricula available.
• Complicating matters further, there seem to be two kindergarten math programs offered by Singapore: Essential Math and Earlybird Math. I’m not totally clear on all the differences or why we should choose one over the other, other than that Essential is less expensive than Earlybird because it does not require a separate teacher’s manual.
• Based on the national curriculum of Singapore, this curriculum emphasizes mental math and application of mathematical concepts, using a highly sequential, logical progression.
• Singapore Math seems to be widely viewed as the most advanced math curriculum available.

I was drawn to this program because of the glowing reviews it received. From all accounts, students who use this program understand math concepts well, know their math facts cold, and can apply any number of mathematical principles to solve problems that are quite dissimilar to the ones they’ve seen before. Students who are gifted in math can be challenged with a quicker pace or with advanced workbooks. Students who are less gifted in math still learn … unless they get too frustrated with the advanced pace, or unless their parent-teacher is unable to decipher the instructor manual’s often inadequate information on how to teach the concept under study. That last one was a sticking point for me. As a parent-teacher who does not feel confident in my own mathematical ability, I prefer a curriculum that will teach me how to teach the concepts; I’m prepared for Jeff to take over Alexa’s math instruction at some point if necessary, but I’d rather it not be before high school. I worry that Singapore Math, with its alternative methods and focus on conceptual understanding, may be a bit on the advanced side for me, the teacher.

Math Mammoth

• Complete curriculum for grades 1-6; the company also offers supplemental workbooks for grades 1-12.
• $36/year for CD or download of the complete curriculum, or $70 for 3 grades. The digital version also comes with the ability to make as many unique worksheets as needed for review. A printed version also is available for a bit more money.
• Worktext system—all the instruction is provided in the workbook, with no separate teacher’s manual required.
• More advanced than many math curricula, though not as advanced as Singapore
• Singapore-style instruction, using multiple methods with a progression from concrete to conceptual understanding within each lesson.
• Focus on mental math and on word problems that require multiple mathematical processes—deliberate, systematic review is built in to the word problems.

Several reviews described Math Mammoth as a significantly less expensive, slightly less advanced version of Singapore Math. Multiple reviews also indicated that this curriculum worked well for their advanced, average, and struggling students—several reviewers claimed to have one of each in their family and said that all did well with this curriculum.  Most reviewers claimed that although students could do this program independently, it was better if the parent-teacher goes through the lesson with the student. Jeff initially had some concerns with the use of multiple methods of instruction (which historically do not have good results in the United States), though those concerns were mitigated somewhat after he read this article.

SPIRAL-BASED OR INCREMENTAL CURRICULA

Saxon Math

• Complete curriculum for students in grades K-12
• One of the most popular homeschool math curricula, it receives high reviews and also is used in many public schools—which could make for an easier transition if we ever decide to put Alexa in a traditional school
• Relatively traditional math program
• It describes itself as “incremental,” and some users are very adamant that it is incremental, NOT spiral. I’m not quite sure what the difference is, but since it seems to be important to them, I mention it in the interests of fairness.

Saxon is either loved or hated; it never is viewed with ambivalence. It’s been a staple in the homeschooling community for an incredibly long time—many who were taught using Saxon now are teaching their own children. Reviews of the program from parent-teachers are stellar: their students memorize math facts, demonstrate outstanding performance on standardized tests, and can do math independently beginning sometime around 4^th grade. However, reviews from former students are much more mixed—while some enjoyed it, many describe a program that they dreaded every day and that killed any love they may have had for math. Tellingly, many also report encountering problems once they entered college: they had learned to apply their algorithms to a series of similar word problems, but they had not learned how to determine which algorithm was needed to solve unique problems or problems that required the use of multiple algorithms. In short, they reported that they had learned to use algorithms, but not to apply mathematical concepts to real world situations. On the other hand, some reported that they were prepared just fine for college math, they understood the concepts well, and they went on to thrive in STEM careers.

Horizons Math

• Complete K-8 curriculum that uses manipulatives, memorization, and drill
• Developed for homeschoolers—it does not assume a traditional classroom environment
• Reportedly an advanced curriculum, though the spiral format causes students to feel like it is not as difficult as similarly advanced mastery programs would be—they learn things in small enough chunks that they don’t realize how much they’re learning.

This math program also is popular among many homeschoolers. Overall, it receives positive reviews, though I don’t recall seeing many that specifically mentioned how good the program is for conceptual understanding or for memorization of math facts. There were several reviews that indicated that children enjoy this program for its variety—each lesson introduces something new, provides practice with that new concept, and then also provides practice with a lot of different types of problems encountered in the past—though an equal number indicated that children felt lost because there were so many different topics encountered in each lesson that students were never quite certain what they were supposed to be learning. Many reviewers also say that the program is good for grades K through 3, but that the 4^th grade level suddenly begins moving more quickly through the concepts, and their students begin to struggle.

Mathematics Enhancement Programme (MEP)

• Complete K-12 curriculum
• Available for free online, or a printed version can be purchased for Year 1 and up.
• This British curriculum is funded by charitable and educational organizations in an attempt to improve mathematics instruction. Because it is British, some modification would be necessary for use with American students (money, for example).
• The program emphasizes logic and critical thinking skills—students are not told how to solve new problems, but are guided in figuring it out for themselves.
• Designed for classroom use, so significant modification is needed for homeschool use.

I first heard of this program while reading in a discussion group related to the science curriculum we’ve chosen—someone asked if there was a particular math program that worked well with Building Foundations of Scientific Understanding, and the resounding answer was that any math program could be used, but that MEP is the natural complement. It seems to be a spiral curriculum that otherwise is very similar to Singapore: a systematic and logical curriculum that is heavy on mathematical reasoning and application and that encourages students to use a variety of methods to solve problems. Unfortunately, though, it also can be difficult for teacher-parents: it requires significant modification for homeschool use and is highly teacher-intensive, which could be a problem for me given my discomfort with math and the amount of preparation required by our science curriculum.

OUR CHOICE

After discussing all the options with Jeff, we agreed that we would try a mastery curriculum first. I prefer to learn—and therefore also to teach—using a mastery orientation, and if Alexa learns well in my preferred teaching style, that will make things easier for all of us.

However, we also believe in contingency planning, so we agreed that if it turns out that Alexa needs a more spiral curriculum, we’ll switch to one. Neither of us were interested in Saxon, with its mixed reviews. Horizons seems fine, but did not excite us. MEP is a better fit. It emphasizes the things we want to emphasize and would give Alexa the best chance at developing a real understanding and appreciation for math. Therefore, if at some point we realize that Alexa needs a spiral math program, we will try MEP, though it is not our first choice.

That left the three mastery curricula under consideration. Although I loved the presentation of Math-U-See, and it would provide the most assistance to me as the teacher, we quickly eliminated it. We simply aren’t interested in a program that often is described as “not rigorous.”

We were down to two very similar curricula. From that point, the choice was easy, at least for next year: Math Mammoth does not offer a kindergarten level, and Singapore does. We’ll be using Singapore Math for kindergarten—most likely Essentials rather than Earlybird, because it is less expensive and I have not heard of any other major differences between them. We have delayed the decision on first grade and beyond, contingent on how well Alexa does in kindergarten. If she loves doing math and does well at it, we may continue with Singapore under the assumption that we shouldn’t try to fix what isn’t broken. If she does well enough but we get the impression that the more advanced Singapore Math may be too much for her, we will try the slightly less advanced Math Mammoth. We may err on the side of trying Singapore rather than Math Mammoth if there is doubt, because it would be easier to switch from the more advanced to the less advanced option rather than the other way around, but we won’t make any final decisions until toward the end of her kindergarten year.

Now we have all the fundamental subjects covered: phonics, handwriting, math, and science. It’s time to move on to the fun stuff: history, literature, religion, art, music, and physical education. Stay tuned, as I’ll eventually write about those as well.

I've Changed

Life is change. Everyone changes, even as adults. People gradually shift their attitudes on a wide variety of topics, often in response to changes in their experiences and circumstances. Usually these changes occur so slowly as to not be noticeable to those with whom the individuals interact regularly, or to the individuals themselves.

Yet, sometimes, people have experiences that change them more rapidly, or in ways that never would have been expected. Moving overseas is just such an experience. I feel much like the same person who first moved to Egypt six and a half years ago, but I’m not. Here are a few of the ways that living overseas has changed me:

I’m More Aware of Culture and Cultural Differences

Not too long ago, a friend here in Kosovo arranged for our family to visit a local Albanian family in their home. Throughout the evening, I plied my American friend with questions about appropriate behavior—is it insulting that we’re enjoying the outdoors rather than the “guest room?” Our hosts seem desperate for us to sit down; should we sit on the blanket they spread on the ground even if we’re more comfortable standing? Should I—and my husband—ask about the extended family, including wives, mothers, and sisters, or should we—he, in particular—not show interest in the female relatives? Is this one of those cultures where I’ll insult my hostess’s cooking if I don’t eat everything on my plate, or is it one in which eating all my food implies that they didn’t give me enough? Is it ok to provide milk for my daughter to drink, or should I allow her to drink the fizzy juice-ish soda? How do I signal that I’m done with the after-dinner tea, or would it be rude to signal such a thing in any way?

When I lived in the United States, in the culture of my birth, not a single one of those questions would have occurred to me. Culture is something that we absorb without noticing it, and we continue not to notice it unless something happens to draw it to our attention—usually an encounter with a culture that is different from our own.

I’m No Longer a Proponent of English-Only Business Practices

On Facebook, a friend posted an account of a personal experience in which she had to “press 1 for English” at an ATM, and she was offended that she had to choose English, rather than the machine’s software assuming she understood it. Before I lived overseas, I would have agreed with her frustration. I was a big proponent of the idea that foreigners in the United States should learn English, and that when we call various institutions, go to an ATM, or engage in other such scripted activities, the assumption should be that we speak English. Now, my initial reaction to complaints of that nature is sympathy—not for the inconvenienced English-speaker, but for the individual whose native language is not English, who needs to obtain information and instructions in a language he can understand, and whose ability to do so could be threatened by proponents of English-only business practices. My Facebook response conveys my opinion on this issue pretty well, I think:

And yet, when we were in Egypt, I really appreciated the "Press 2 for English" option. I'm inclined not to mind giving the same courtesies to non- or limited-English speakers in the United States that I've enjoyed as a limited-Arabic speaker in Egypt, a non-Khmer speaker in Cambodia, and a non-Albanian, non-Serbian speaker in Kosovo … It's much more efficient for everyone involved—incuding that native speaker in line behind the foreigner who's taking forever because he doesn't understand anything on the screen—to have the ability to choose the language right at the beginning. It takes 1 second of your time to push that button for English. As someone who has desperately needed that button before, I sympathize with those who need it in the U.S.

I Notice and Am Angered Annoyed By Unwarranted Exaggeration

I’ve lived in a country that was an effective dictatorship—I’m no fan of President Obama, but don’t tell me he’s a dictator. I’ve lived in countries where corruption is just the way things get done—certain parts of America have more corruption than others, but rule of law is the norm; don’t tell me that America runs on corruption. I’ve lived in countries where the poor have multiple generations living in one-room houses with dirt floors, no electricity, and no plumbing, and where allowing any one person to eat his fill means that another family member dies of starvation—don’t tell me that a person with a comfortable home, plenty of food, and cable TV is poor. I’ve lived in countries where the lucky children attend trade schools rather than so-called “academic” ones (that don’t actually teach anything), so that they can earn enough money to keep their younger siblings from starving while learning a skill that will enable them to make a decent (for their country) living as an adult—don’t tell me that these kids are slaves because they’re being paid less than you would accept for similar work. I’ve lived in a country where people may be killed for becoming Christians—don’t tell me you’re being persecuted when your employer wants you to work on Sunday or when the decorations at City Hall say “Happy Holidays” instead of “Merry Christmas.”

My Foreign Policy Opinions Have Changed

When I lived in the United States, it was easy to decide what the official foreign policy of the United States of America should be: whatever was in our best interest, period, no further questions asked. It all seemed so clear cut. However, when I started paying attention, which for me was when I moved overseas, I began to see more shades of grey than black and white. I still believe that American interests should dictate American policies, but it isn’t always clear what those interests are or how best to advance them. Many fiscal conservatives—including me at times—reflexively oppose foreign aid, for example. However, I’ve learned that sometimes foreign aid is exactly what is needed to shift the attitudes of a population toward American interests, so that they are more likely to assist us in accomplishing our goals in the future. Don’t get me wrong; I have no problem making foreign aid conditional on the policies of the assisted government, such that governments that oppose U. S. interests find themselves with less—or no—aid, but even there, the situation often calls for more subtlety than I once appreciated. I’ve realized that it’s easy for those of us with only headline-level information to think we know the best course of action, but once we get into the details, it isn’t so easy to make sense of the complexities and apparent paradoxes, and the best decision becomes less obvious.

I once had sympathy for American isolationists who wanted to let the rest of the world deal with their own problems. Now I recognize that the problems of the rest of the world often are our problems, though they may not be knocking on our doors just yet. (Think Ebola—what if we’d helped contain this outbreak when and where it started, rather than waiting until it came to the United States? It would have been a lot easier to deal with it then.)

I Have a Heightened Appreciation for the United States—Warts and All

Some of the above sections may make it sound like I have lost sympathy or understanding for my fellow Americans, or like I have lost my perception of the United States as an exceptional nation, or that I have lost the ability to recognize flaws that exist in my own country. None of those is the case. The good in America is there, and the bad in America is there, and living overseas, where I can see the good and the bad in other places, has given me the eyes to see both more clearly.

I have a much greater appreciation for those things that make our nation great. The United States was established on the freedom of the governed to choose their leaders, and despite the bellyaching of both political parties at various times in our history, that foundation is not and has not been in jeopardy. Our educational system puts to shame the educational systems of so many of the world’s nations. Our economy, even in the tough times, allows us to enjoy prosperity to a degree of which most of the world’s citizens can only dream. And despite the fact that our medical care is not provided for free as so many would prefer (I wouldn’t prefer, but that’s neither here nor there), the quality of the medical care available in American hospitals—even those with less than stellar reputations—is head and shoulders above the care available throughout most of the rest of the world.

As for America’s warts—I recognize those, too. I recognize that our culture is such that it makes childbearing and rearing more difficult than it needs to be; that community is lacking in most American cities, towns, and neighborhoods; that our prosperity has led to a materialism that cannot and should not be sustained; that the stereotype of the arrogant American exists for a very good and very regrettable reason—that too many Americans overseas expect the world to adapt to them, rather than recognizing their obligation to adapt to the world. There is corruption; there is political overreach; there are things that can and should be done better.

I know that when I go back home, when I visit my family, even when my friends and family see my Facebook posts or read this blog, they see that I have changed. I have become more complex in some of my attitudes, more simple in others. I have become more liberal in some ways, and more conservative in others. I’m pretty sure that not everyone likes all the changes—and frankly, I’m not always sure that I do, either. But overall, I have to say … I like who I’ve become in the last six years. I like that I’m willing to challenge ideas that I used to accept unthinkingly. I like that my default response to inflammatory headlines now is to dig deeper and try to find out what’s really happening. I like that I look for commonalities and try to understand individuals as individuals, no matter their nationality. Others may not need to leave the country of their births in order to experience these changes, but I did. And I’m glad I did.