Tonight was the School Board meeting in which some data were shared about our current SCASD students’ math fluency skills, performance on some locally developed math assessments, and AIMSWeb probes (more on that later). When I came late after the meeting, I ended up talking at length with our wonderful sitter, a recent graduate of our very own SCASD high school. He became very interested in what I’d been doing tonight speaking to the board and why I was so invested in seeing things change.
“I’m really glad you’re doing that,” he said, and sheepishly admitted that – as a sophomore in college — he was struggling in his entry-level statistics class. Why? Well, he is not allowed to use a calculator on exams in the class, and he struggles with long division and multiplying decimals. He indicated that he watches some kids after school and was unable to even assist a 4th grader with his math homework on division. To further prove his point, he offered to do some problems for me, and — sure enough – he’s right. He had no idea where to start to answer 3156/27, and while he could do the multiplication involved for 43.6×21.4, he didn’t know to move the decimal in two places and moved it only one. Oh, dear! Lastly, he indicated that he still finger counts to do basic addition and subtraction. His hypothesis about the key to his difficulties: he was handed a calculator in 6th grade and has been using it ever since, so he NEVER MASTERED THE BASIC MATH FACTS OR CALCULATIONS BY HAND!!!!????? Can you imagine? Do you think that testimonies like this would be enough to sway the board? One could only hope so.
I am absolutely sickened by this, and my heart goes out to him and others stuck in his position. I feel horrid that he has a high school diploma from our district and yet doesn’t have the foundational math knowledge or procedural skills to be successful in a lower-level class required for his major. Truly, he is another heartbreaking example of a curriculum casualty. We absolutely cannot allow this to happen to any more of our kids!
(For the record: This student gave me the OK to share his story, so I am doing so with his permission. We talked at length about academic supports available on PSU’s campus, and other strategies he could use to address his educational needs. I really hope he can get the help he needs both in the short term and beyond!).
That is really tragic, but will not be surprising to anyone who teaches math or science at Penn State. I often encounter students who reach for a calculator when they have to find the answers to questions like 400/10. This has happened with students from SCAHS and, sadly, from districts all over the state. When I ask such students to try it without a calculator, I can see that they are embarrassed – they know that they have missed out on something somewhere along the way.
I had plenty of experience with the low math skill of the PSU students. As a faculty at the math department, I had chance teaching undergraduate math courses, such as calculus, differential equations etc. Exam grading is often a depressing time. I have seem answers such as 4+4=16, 6+8=16 etc. (Not to mention multiplications such as 15×8. No way.) Although I understand the pressure during a test, but this is beyond the lowest expectation. (My daughter would never have messed this one up, not even in 2nd grade.)
Barb — A couple of points:
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.
Jim,
Your example of the Stanford student does indeed falsify Barb’s “proof” that the existence of a SCASD graduate who cannot multiply implies that we have a poor math program. The problem with your statement is that Barb never said that her story constituted a “proof” of anything.
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
Fifth graders’ low rates of fluency with multiplication and division facts as presented on Monday, combined with the fact that long division is not taught by Investigations but is now patched in by the ‘action plan’ may mean that moving on to Connected Math (and its embrace of calculator use) in grade 6 may put these kids at risk of similar outcomes to those described in my original post.
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.