Interesting research on calculator usage using a small sample of third graders by Rittle-Johnson & Kmicikewycz (2008) suggested “that the generation effect [solving problems by hand rather than using a calculator] may also improve learning and transfer of procedures, at least for people with low prior knowledge. The generate condition improved success on unstudied multiplication problems as well as on studied problems, suggesting that the children with low prior knowledge had developed or refined procedures for multiplying such as repeated addition” (p. 80). Their conclusion: “Initial practice in generating answers seems important to
support procedure acquisition; once procedures are learned, the benefits of generating answers
may be reduced or eliminated. This converges with teachers’ beliefs that ‘‘calculators should be used
only after students had learned how to do the relevant mathematics without them” (Ballheim, 1999, p. 6).”

This presupposes that fluent, practiced, procedural acquisition (e.g., on efficient algorithms such as long division) occurs with immediate feedback from instructors. Given what I’ve seen of Investigations, I’m not convinced that it does.

I would argue that people like this student who pass through SCASD successfully with grades good enough to go to Penn State but without being able to do simple computations are an indication that something is wrong. You are absolutely correct that this college sophomore would not have been in Investigations, but I am sure you are aware that he would have gone through three years of Connected Math, the curriculum we have used in grades 6-8 since 1998 that is notorious for its reliance on calculators and for being evaluated recently by the U.S. Dept of Education as having “no discernible effects on student achievement”.

Let’s turn back to the Stanford student. As you suggest, the fact that such students come out of SCASD does not “prove” that SCASD is doing a great job with it’s math program. Similarly, when an airliner lands safely, that doesn’t prove that the airline is doing it’s job with respect to safety inspections. But when an airliner crashes and the cause is determined to be failure of a part that was certified as safe in a recent inspection, there should be consequences.

You wrote that this story doesn’t “make the case” and again, you are right, but that does not mean that there is not an overwhelming case for changing how we do math in SCASD. On Tuesday you heard that despite weekly and sometimes daily access to computerized fact practice, only 28% of SCASD students at the end of third grade are proficient with addition, the second-grade standard. Think about this: 72% of students at the end of third grade cannot answer sums to 20 (3+4, 5+7, 9+8, etc.) in four seconds, the test specified by the very people in the District who are proponents of Investigations. Look at a clock with a second hand for four seconds – it’s a lot of time, enough time to conclude that if you don’t know 5+7 in four seconds, you don’t know it.

There are not as much data as we might like on math curricula, but all that we do have point to the same conclusion. As a reader of the PQME blog, you will already be familiar with much of what is known from assessments of our own kids locally and from the literature, so I am not sure I need to recount it here.

Let me ask you the same question I asked to the Board back in December – if what you have seen so far does not motivate you to ask for a change in the SCASD math program, exactly what would?

-Steve Piazza

1. This young man is not unlike many of the folks I used to teach in MIS. Just calculating the rate of transfer on a network was viewed as higher math. There are many students like this guy. My brother was like this guy. We both had the same “new math” curriculum at the same school with many of the same teachers but with very different outcomes.

2. If he is a sophomore at Penn State, he never had Investigations; he had a previous curriculum. I could in turn cite my neighbor’s daughter who was taking Senior level math courses at Stanford as a first year student. Both she and your sitter had the same SCASD curriculum, but each had a very different outcome. That is the danger of proof by anecdote.

3. It is sad that as you say he “doesn’t have the foundational math knowledge or procedural skills to be successful in a lower-level class required for his major.” Math as we know is a gateway subject. His is a perfect example of where that gate is mostly closed. Penn State does provide plenty of academic assistance for our students. He should probably look into this right away.

4. While his is a sad story, it really doesn’t make the case for or against the current curriculum.