UH Hilo mathematician Mitchell Anderson: How does the Common Core State Standards impact the Hawai‘i community?

The Hawai‘i Common Core math curriculum this year is of a higher quality, fits better into the time constraints imposed by teaching schedules, and is being adopted by even more teachers.

COMMENTARY

By Mitchell Anderson

Note: Mitchell Anderson, associate professor of mathematics, will be doing a public presentation on Wednesday, Nov. 19, 6:30-7:30 p.m., on campus at UH Hilo in UCB Room 100, where he will address “Common Core Standards: What does it mean to you?”

Mitch Anderson
Mitch Anderson

Standards for K-12 were first introduced in US schools in the early 1990’s. It was at that time that the national educational communities began questioning if our educational system was delivering to our students that which we purported. In mathematics the university communities were questioning our calculus delivery, and that questioning gave rise to the Calculus Reform Movement. Educators began identifying student learning outcomes (SLO), which identified desired learning outcomes that we had for our students for each course; and assessing those SLO’s came into vogue. Every state across the nation had their individual sets of standards. It was a learning process, and many of the standards left a lot to be desired. Their orientation for mathematics was primarily content, in the form of topics to be covered, and process-oriented skills. This was counter to what I had known from 1985, and counter to the Calculus Reform philosophy — that it was not enough to teach students “how” to symbolically solve problems using algebraic techniques. A minimum requirement must be that students truly understand the major concepts, and how to interpret their symbolic manipulation results in real-world context.

In the early 2000’s a bipartisan group of governors and business leaders proposed that we develop and adopt a common set of standards. It is difficult to pin down their motivations. Some say that it was a waste of money having every state develop and redevelop individual standards. Others say it was politically motivated, while still others say that Bill Gates wanted a more stable supply of computer programmers for Microsoft. Whatever the motivation, it was clear that we as a nation were falling further and further behind in education. The U.S. currently ranks 30th in the world. In 2009, The National Governors Association, the Council of Chief Education Officers, and 48 states asked a national non-profit organization called Achieve to develop a common set of standards. Starting with the best state standards, with broad input from teachers and education leaders, three authors took charge and wrote the K-12 mathematics standards. It was a recursive process, with broad input from teachers and feedback from the general public. In 2010, they presented their work in the form of the Common Core State Standards (CCSS). Forty-five states to date have adopted the standards for use in their schools.

Since standards were first introduced in 1990 I had reviewed numerous versions, and they never failed to disappoint. The process in which the standards were produced was sometimes chaotic, at other times nonsensical, and in all cases I was not impressed and they ended up in the garbage. I was very much pleasantly surprised when I first viewed the Common Core State Standards, recognizing that these were drastically different. I had always wondered how to teach high school mathematics from a conceptual perspective, as I do in college, and the CCSS immediately revealed to me how that was possible. The high school mathematics common core standards are not a listing of topics to be covered in Algebra I, Geometry, Algebra II, etc. Instead, they are a set of standards that are grouped in clusters of similar concepts and skills that students must master throughout high school. Unlike grades K-8, the high school math standards never mention a specific grade or course. The concepts included therein are concepts that students might encounter in multiple topics within Algebra I, for example, but that they might also encounter in Algebra II or beyond. More than half of the standards were more conceptual than skill-based, and this represented a tremendous shift from previous standards.

Initially this surprised me. Later it amused me, and then it scared me. It amused me because it is my experience that there are more traditional educators across the country than progressive ones. Traditional educators teach their courses in a manner similar to the ways they were taught, primarily by traditional teachers who learned from traditional teachers, who in turn also learned from traditional teachers. It is a self-perpetuating problem. Much of the mathematics that was taught in the high schools prior to the common core has been taught since the slide rule era. This in itself is not surprising; after all, how much can mathematics change? Not much, at least not in terms of the concepts. However, much of the skill-based mathematics resulted from an inability to compute numerical approximations to “exact” answers. Thus, students needed to manipulate the symbols to a point they could apply their slide rules. Yes, much of the high school mathematics typically taught in the high schools before common core came from the slide rule era. And, because of the self-perpetuating problem, the teachers could not be convinced that they were no longer important. Furthermore, what should be taught instead?

As an example I offer the process of “rationalizing the denominator.” I’m sure the reader remembers being required to rewrite fractions so that no radical resides in the denominator. This was required because performing long division with an irrational number divisor was quite cumbersome. So, the denominator was turned into an integer and the irrational number moved up to the numerator. This made division much easier, with the use of the slide rule and tables of radicals found in the back of the book. But, we’ve been able to use a scientific calculator to quickly get approximations to these types of numbers since I was in high school back in the 70’s. Yes, this unnecessary process was still around 40 years later! Factoring expressions in order to solve equations is yet another example of a skill that needed to be mastered in order to solve equations. Factoring typically sucked up an inordinate portion of the school year. However, most equations in the real world do not factor; so students spent a tremendous amount of time mastering a skill that would only work on contrived book-problems. Today students can use graphing calculators, computers, and iPhones to solve equations in seconds that students of the past century would never have been able to solve in college, let alone high school.

So, what does the shift to CCSS mean to Hawai‘i students? I would now like to bring you back to an earlier comment I made above, that I became scared when I thought about the standards. The standards represent a radical change. As such there are no textbooks that currently reflect these new standards. Allow me to repeat that. There are no textbooks that reflect the high school math standards. This is still true today. Therefore, teachers would be expected to teach to the standards without the help of textbooks. This would be very difficult. First, the standards are not grouped by topics. In the past teachers would teach a standard and then move on to the next. These standards are not intended to be used in such a manner. They more closely represent a philosophical shift. They provide more of an orientation of how the subject matter should be taught, and they do not represent a road map of how to get there. That was left up to each state. Second, they are widely open to interpretation, and they are not prioritized. As an expert in the field I even struggled identifying some of the subtleties found therein. The more I contemplated the standards the more I came to the conclusion that the teachers were going to need help, a lot of help. They were going to need a roadmap, instructions on what to teach, and the orientation of how each standard fit into the whole high school mathematics curriculum. First off, they were going to need a course outline for each standard course.

I decided to develop a detailed course outline for Algebra II, and therein identified which standards would be addressed where. I presented it to the Hawai‘i Department of Education and suggested they were going to need something of this sort to help the teachers. They contacted me and requested a meeting, right away. They had been struggling to determine just how to roll out the high school Common Core across Hawai‘i, just as was the case with most states across the country. I called in Dr. Roberto Pelayo of the UH Hilo math department and Dr. Diane Barrett of the UH Hilo education department to join the meeting. It was decided at this very first meeting that we would identify a team of master high school teachers and together write day-by-day lessons for use in the classroom in fall 2013. Halfway through the year the DOE requested we do the same for Algebra I, for simultaneous rollout. The new curriculum arrived mere weeks before each quarter, and included daily handouts, homework, lesson plans for the teachers, and assessments. Finally, we offered quarterly training sessions to all Algebra I and II teachers, in which we went through the lessons one by one to help them understand the new orientations this new curriculum represented.

During the first year it was estimated that approximately 50% of Hawai‘i’s Algebra I and II teachers adopted the curriculum across the state. The first year’s curriculum was a first draft, and while it was generally well received, it still needed work. This year the three UH Hilo professors conducted major revisions, taking into account feedback received from the teachers. The curriculum this year is of a higher quality, fits better into the time constraints imposed by teaching schedules, and is being adopted by even more teachers. The state DOE assessment office contracted a national assessment organization to independently develop and administer end-of-course exams for both Algebra I and II. These exams were administered to all students in these courses across the state in spring 2013 and spring 2014. The results for spring 2014, the first year teachers utilized the new material, indicated a 10% improvement over the first year, in both courses. This exam is now being used to determine a portion of each student’s final grade. It is anticipated that as more and more teachers adopt the new curriculum, and those that have been using it become more familiar with it, the scores will continue to rise.

In 2015, national exams developed by two non-profit organizations will be administered to all 11th graders in most states. Every Hawai‘i 11th grader will join the 11th graders from 25 other states to take the Smarter Balanced Assessment Consortium (SBAC) exam in the spring of 2015. While we do not expect Hawai‘i to rank the highest in the nation, it is our hope that Hawai‘i will rank higher in the country than in the past. We base this hope on the fact that all states are struggling to implement the Common Core, and Hawai‘i has one of the more comprehensive common core curriculums in the nation.

In addition to the Algebra I and II revisions, the three UH Hilo professors are currently developing Common Core curriculum for Geometry, which is intended for use in fall 2015.

Mitchell Anderson is an associate professor of mathematics and senior mathematics department member at the University of Hawai‘i at Hilo. He is one of three primary authors of the Hawaiʻi Common Core high school mathematics curriculum, and was a driving force behind its inception. He has had considerable input into developing the Smarter Balanced Consortium’s national exam (SBAC), which is set to be administered to all 11th graders across multiple states beginning this academic year. Contact.