For some people and classrooms, it just isn’t feasible to purchase high-quality number bond flash cards like you can obtain through Crystal Springs Books. I came across a site where you can download your own, print them and cut them out. These are addition and subtraction cards appropriate for grades K-3. You can download them for free after registering at Teachers Pay Teachers. A caveat: While the free cards by William Hughes cover the basic principles of number bonding for addition and subtraction for numbers to 10, the Crystal Springs cards are better because they do not rely on just…
This homeschooling website has an article about Singapore Math that is short but informative. It tells a brief history of Singapore Math in the US, then goes into why it may or may not be the best choice for a homeschooling curriculum. Here is an extract from the article: The curriculum uses a true spiral approach, a method that is used less successfully in the United States. In the spiral approach, the curriculum assumes prior mastery of the subject in the previous grade and so does not review basic processes but moves on to a higher level in each subject.…
I’ve been reading blog posts about math like this one, in which a common theme is that we need to return to “basic” or “regular” math skills and dispense with the constructivist programs that were so popular in the last decade or two. I’ve read about people who are frustrated with the idea that children should have to reconstruct the math theorems that evolved over the last 2000 years or so, and it makes sense that they shouldn’t have to do this. Some people turn to Saxon Math, which I have taught, or Singapore Math, as the solutions that teach…
There is an interesting website devoted to reforming math education in Utah; it is utahsmathfuture.com. On it, among other text and video content, there are links to reports about a longitudinal study in a Massachusetts school district showing the improvement in test scores over the long term when the district adopted Singapore Math. The evidence is compelling, not only qualitatively but quantitatively. I have also provided the report for download here.
If you are a parent who is interested in how Singapore Math works, but you don’t have time to attend a training session or do a lot of reading about it, here is a resource for you. This school recorded a session in which their parents were taught how this program works and how to support their children. Part 1 of the videos is here; click the video to go to Youtube to view the other parts.
A New York Times Magazine article titled Building a Better Teacher appeared last March. It’s an excellent contribution to the debate about what makes a good teacher. As the article describes, it’s not enough to care a lot; there are many caring teachers who can’t get their students’ attention to teach them anything. Being a good teacher is not strongly correlated with the graduate schools they attend, their teacher test scores, or particular personality characteristics. None of these predicts teacher effectiveness well. Merit pay and high pay incentives, haven’t worked to improve teacher quality (or test scores) either. In fact,…
This is the first year since 2003 that I will not be teaching NaNoWriMo in the classroom. What’s good about this is it frees me up to do it with a whole bunch of area students. I have posted a new program description for our fun, exciting adventure to come. Here are a few details not included in the program description page: Each student will get to set his or her own word count goal, usually with some consultation with me. That goal can be fairly flexible to a point in November. The idea of the program is to write…
Imagine trying to pay for a doughnut and not knowing if a $10 bill is enough. Imagine not knowing which is more, 5 or 4. Imagine never having a sense of time, so you are always early or late for things. Or someone gives you an hour to complete a task, and you have no idea how long that is or how to pace yourself. Imagine never being able to retain the difference between left and right. Imagine being in high school and understanding the concepts of algebra, but being unable to do basic addition and subtraction, let alone the…
The Urban Word of the Day today was “cerebral bulimia,” defined as “binging and purging of the brain.” Doesn’t that sound familiar? It calls to mind all the useless studying in which facts are crammed into temporary storage in the brain, dumped out on paper (or computer) for a test, and promptly forgotten. This can, of course, include math algorithms and formulas. How different it is when, like an athlete learning what works best for her body, we learn the fundamental concepts behind new ideas first. Then the algorithms and formulas follow logically. It can even be possible to recreate…
New York State is putting teachers and students under more pressure by revising the required scores on standardized tests for students to achieve proficiency. Why are they doing this? Apparently it is because despite passing Regents tests, almost 25% of the students need extra support once they reach college. How will they afford “remediation” for all the passing students who are now failing? One more sign of why it is so important to put conceptual understanding ahead of rote application of algorithms. It is easy to forget what one learns by rote, but not deeper conceptual understandings. Here is a…