November 16, 2015
Students Can Subtract Confusion from Math Standards
By Sahar Mohammadzadeh
It doesn’t take anything more than a multi-step subtraction problem to result in a wide spectrum of reactions including Facebook posts from confused parents going viral. But there is a reason behind the creation and implementation of our state’s math standards, and it is not a mystery.
Math is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. School curricula should be designed around correlated progressions from grade to grade so students can build new understanding on previously built foundations, a more expanded and realistic representation of mathematics than what today’s adults may have experienced in their formal schooling years.
With this goal in mind, the newly adapted mathematical standards are benchmarked to the standards of the top education systems in the world, including Finland and Japan. They are designed to address the problems of a curriculum that was “a mile wide and an inch deep” by building upon the most recent studies on how students learn and retain information. These standards are about developing ways of thinking alongside ways of doing. The two work hand in hand.
The Student Voice Team put the newer standards to the test when we visited a third-grade classroom at Red Oak Elementary School in Nicholasville. We watched as the students were presented with a problem to solve.
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Mrs. Burns, the teacher, requires her students to derive the solution though both multiplication and addition with an emphasis on an analytical development process asking them to explain not simply what they got but also how they got their answers. She focuses on a process that emphasizes the difference between knowing how to solve simple multiplication problems and determining whether multiplication is the most efficient strategy.
Through a vocal, systematic methodology the students are able to break apart the day’s learning target. We heard one say: “I can multiply a whole number up to four digits by a one-digit number.” We witnessed Mrs. Burns explain how to solve up to four-digit multiplication problems through partial products – a concept usually reserved for higher grade levels and were impressed hearing her use words like “misconception” and “efficient” with her rapt eight and nine-year-olds.
Fast forward a couple of years into high school and you might run into me, a sophomore at Paul Laurence Dunbar taking AP Calculus BC. As a student in a magnet program specifically targeting future professions that relate to mathematics, I thoroughly understand the importance of comprehension, explanation, and proofs when learning new, abstract ideas. In calculus, we are currently working on understanding the intricacies of antiderivatives and integrals. The concepts are deep and challenging, but our teacher takes the time to develop the required conceptual understandings as well as the multiple strategies we might use to solve problems.
In a process resonant with Mrs. Burns,’ my teacher introduced the topic of integrals and solved a sample problem using two different methods. By the end of that class period, not only did we have multiple tools in our arsenal, but we had also mastered how to use them. We understand that mathematics is an abstract flexible topic that is not constricted to a finite set of rules and theorems.
Kentucky’s mathematical standards are mimicking these higher-leveled environments, deepening the contextual understanding of numbers and equations. Proficiency in these skills plays an imperative role when it comes to preparing all students for a successful education, whether they chose to pursue a further interest in the subject or not. It is no stretch to imagine that when Mrs. Burns’ third graders do reach a higher level, they can accomplish great feats with great ease since they have been making these advances all along.
With an increased focus on conceptual understanding, procedural skills and fluency, and relevant application, elementary students – like those at Red Oak – are taking command of mathematical concepts: learning, doing, teaching. Rather than racing to cover many topics superficially, Kentucky’s academic standards ask math teachers to significantly narrow the way time and energy are utilized in the classroom by focusing deeply on specific concepts for each grade level.
Because Kentucky’s math standards may not hew to the way they were taught, many parents have understandable frustration in trying to decipher the thinking behind them But if it’s assurance they’re after, rather than turning to Facebook to clarify the seemingly fuzzy math, might they consider listening to some informed classroom voices instead?