Kentucky’s Prichard Committee for Academic Excellence has always been ready to blow its happy horn for Kentucky’s schools – regardless of those schools’ actual performance.
A new case in point just arrived with Prichard’s short paper, “Finding Solutions, Standards Push Students Toward Real-Life Problems.” This paper focuses on the way:
“Kentucky’s standards for learning in math and English language arts, adopted in 2010 and now everyday practice for teachers and schools across the state, aim to create more challenging and relevant learning experiences for students.”
However, the middle school teaching examples from the South Warren Middle School in Warren County gushingly described in the paper leave me and some noted national math experts wondering what Prichard is thinking – especially since the example exercises don’t seem to align with Common Core and don’t appear to be grade appropriate.
Furthermore, the most recent test results from the eighth grade college-readiness-related EXPLORE assessments show math performance in this school fell during the 2014-15 school year.
So, why should we be impressed?
Among other things, the Prichard paper talks about several seventh grade math exercises used by South Warren Middle School teachers.
In the first example, the teacher screws and nails boards together and then takes them apart – somehow – as a way to teach fractions. In the second problem, also somewhat poorly described, students weigh out pennies on a scale as they – somehow – supposedly determine equivalent numbers.
Nationally known math expert Professor James Milgram from Stanford University, a member of the Common Core State Standards Validation Committee, said the descriptions of these exercises are unclear:
“I looked over the examples briefly, and was totally confused by their description. My guess: they are complete nonsense.”
Ze’ev Wurman, another national math expert who’s a former member of the US Department of Education and visiting fellow at the Hoover Institution, echoes Milgram’s concerns:
“It makes no sense, unless someone believes that working with boards, hammers, and nails is inherently conducive to mathematics (smile). Otherwise using simple algebra or number tiles would achieve the same, albeit without the noise of hammering.”
“More importantly, the teacher seems to focus on developing the meaning of number, fractions, and operations in grade 7, which — by Common Core itself — should be all finished by grade 6. In fact, the things the teacher seems to be doing (related to the ‘meaning’ of a fraction) are actually grade 4-5 content.
All I have seen from Common Core ‘successes’ so far were teachers gushing over student being ‘deep’ and ‘insightful’ over content 2-3 years behind.”
While we at the Bluegrass Institute certainly support truly effective and innovative teaching techniques, Wurman’s charge that the examples in use at South Warren Middle School were below grade-level techniques caught our attention. For sure, we’ve heard lots of claims about similar teaching approaches since KERA began a quarter-century ago that just never panned out.
To confirm Wurman’s comments, I dug up Kentucky’s Common Core standards for various grades, and sure enough, the South Warren County seventh-grade use of “manipulatives” to teach fractions seems well behind what even Common Core requires.
Here are some examples of Kentucky’s actual standards on fractions and their relationship to the South Warren County Middle School seventh-grade exercises:
Grade 3 Standard: “They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators (emphasis added).”
It’s clear that using manipulatives as a teaching tool for fractions is supposed to begin in the third grade.
Grade 4 Standard: “Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions (emphasis added).”
This sounds a lot like the Prichard paper’s seventh-grade example where kids are weighing out equal amounts of pennies on a scale, doesn’t it?
Grade 4 Standard: “Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number (emphasis added).”
Hmmm. That composing and decomposing of fractions sounds a lot like what the South Warren teacher was doing with seventh graders when she was nailing and screwing boards together, doesn’t it?
Grade 6 Standard: “Apply and extend previous understandings of multiplication and division to divide fractions by fractions.”
Whoa! This goes way beyond using manipulatives. Here students are doing serious math with numbers, and at a much more sophisticated level than the South Warren Middle School example.
Finally, here is what students should be doing by Grade 7 in Kentucky:
Grade 7 Standard: “Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.”
That’s much more complex than anything South Warren Middle seventh graders were doing.
I got an interesting letter about the first edition of this blog that made me wonder: why would a reportedly respected teacher be using techniques that Common Core calls for in much lower grades?
I realized the answer could be related to a real deficiency in the Common Core State Standards. That deficiency is the absence of any “Scaffolding” plan to transition students from the old, less-demanding programs they formerly were receiving into what – for Kentucky, at least – is the more demanding Common Core program. Quite likely, most students in the seventh grade today never got the background math instruction that Common Core assumes occurred in the lower grades. Very simply, the students are behind and need those lower-grade teaching techniques to catch up.
Furthermore, the teacher had to invent this scaffolding on her own because the Common Core group apparently never even considered this important issue.
To be sure, that does not excuse the fact that Kentucky’s kids clearly were not getting the math instruction they needed before, but it does explain why more than three years into the Common Core program a teacher might have no choice but to offer below-grade-level types of assistance.
This readiness issue, however, creates a real puzzle for me about something else found in the Prichard paper. This involves the discussion of an eighth grade math example where students are exploring exponential functions.
However, the Kentucky Core Academic Standards don’t introduce exponential functions until high school. The eighth-grade standards only cover “the connections between proportional relationships, lines, and linear equations (emphasis added).”
A PDF word search of the Kentucky Core Academic Standards indicates that “exponential functions” are not discussed in any standard below the high-school level.
Could it be that South Warren Middle School is taking kids who are behind in fractions in the seventh grade and then trying to jump them far ahead with exponential functions just one year later?
Could this explain why the school’s eighth grade EXPLORE math score, which was 16.5 in the 2013-14 school year, dropped a full half-point to 16.0 in the current 2014-15 school year?
Unfortunately, that score drop seems to makes sense. Why Prichard tries to fool us about this school – whose eighth grade students could be getting more confused about math – and about Common Core, however, is a great puzzlement.
(Updated June 5, 2015)