- Why So Few Units?
Because math is not a race, it is a process. It should not be rushed. The reason 1/3 of all our students fall behind in math is that they never get the time they need. Rather than getting to develop understanding, they turn to the next best solution — “Just tell me what to memorize.” By 4th or 5th grade, they have a jumble of algorithms that they confuse/ forget and they have learned to distrust their own ability to figure anything out.
- Why 3 months of Fractions?
Firstly, we do other things besides fractions – patterns, word problems, investigations. Secondly, it’s actually a whole year of fractions! We usually do at least one fraction problem a day (like a vitamin!) – all year long. Why do fractions take so long? Because our approach is visual and builds a solid understanding of fractions, not a hodgepodge of easily forgotten algorithms… and because fractions matter.
- What is a “Sandwich Unit”?
Some units are so important (multiplication in 4th grade, fractions in 5th, negative numbers in 6th) that they should receive extra attention in the curriculum. In 5th grade, we approach fractions (and word problems with fractions) immediately in September, but we keep them as concrete/visual as possible, using the bar model approach. Then we run those fraction concepts ‘in the background’ on homework as we go through the rest of the year. There’s at least one “Draw this fraction problem” on each homework for months. In many cases, these problems cover material that has not been taught – the model drawing tool provides solutions. This gives everyone time to master concepts and develop insights before we move on to the fraction algorithms late in the school year. (Hence the ‘sandwich’ metaphor – Start fractions in September, run them in the background for months, then return to them in May.) Many students who thought they could add fractions (algorithmically) find they cannot actually draw them – they haven’t internalized what fractions truly mean.
- What about gifted students?
As you will see, our units include challenge work, on a daily basis. It is one of the strengths of Singapore Math. It consists of thinking challenges, not just ‘more algorithms – faster please’. The goal is depth and curiosity.
- What about standardized tests?
We don’t even know where to start here. Is education about learning or politics? Are tests justified in math if (by definition) a third of our students fall below expectations? Breaking from over-ambitious curriculum expectations takes courage, but in fact, after 15 years of using Singapore Math at our school, we have seen an increase in number sense, word problem skill, algebra-readiness, and yes, incidentally, in test scores. More of our 8th graders end up ready for Algebra I than ever before – even students who (two decades ago) would have failed at math and given up. They now choose the 4-year course path most suited for them in high school and they flourish. What more could we ask for?
