Kyla Giffin | Editor-in-Chief
My earliest math-associated memory can be traced back to a day in the second grade, where I sat among the small desks, ancient globs of gum stuck on their undersides, scratches and pencil markings lining their edges. The class was learning how to calculate time–a concept that plagued my seven-year-old mind to the point where I began to shed many a tear.
To put it simply, mathematics was not my strong suit starting off. It was not until third grade when my teacher opened me up to having a much stronger comprehension of math. She would take aside a group of students who did not understand the material after the lesson, in order to more clearly elaborate on it, leaving the other students to start their classwork. I can still recall the day we learned long division, when I leaped up from among the other confused students with ecstasy, as I realized that I was, in fact, no longer perplexed.
Third grade was a turning point for me, and in fourth and fifth grade I was one of the more mathematically advanced students. This was the start of a series of rigorous math courses, for when I entered middle school, I was suddenly propelled into a math class that had been created for advanced seventh graders–Pre-Algebra: a somewhat unexpected and challenging impetus, but one that I more or less thrived with. In seventh grade, I took Algebra 1, and in 8th grade, I was in Geometry.
Taking Algebra 1 and Geometry in middle school had set me up for being able to have six years of math under my belt by the end of high school. However, middle schoolers in the Livermore Joint Unified School District may find this to be a more difficult feat to accomplish with the changes to their math courses that occurred during the 2013-2014 school year, and continue to be in existence now.
“In 2013-14, new courses were offered to align to the new standards and also included new textbooks,” said Robyn Schlichter, who is in her ninth year as District Math Coach here in Livermore. “The [California] Content Standards for Math introduced a new middle course, Math 8, where some of the old algebra topics are now taught…and consequently, some Algebra 2 content was pushed down into Algebra 1. This change has increased the expectations of what students know at [this] level.”
Schlichter continued, “In addition, we added two new middle school math courses: Accelerated Math 6/7A and Accelerated 7B/8. These two courses are specifically designed for students who excel in mathematics and would like to complete more math courses.”
But what led to such modifications–more specifically, what were the new standards? According to Schlichter, “Course changes were initiated by the adoption of the California Content Standards for Mathematics [in] 2010. The new standards increased the rigor of mathematics at lower grade levels to prepare students for success in mathematics at higher levels, ultimately to be college and career ready. This change was not just a change in the ‘what’ was taught, but also in the ‘how.’ Students are required to not only solve arithmetic, but to think critically, collaborate with others, and communicate their reasoning through oral or written explanations.”
These were the goals set out to be accomplished. Now, four years later, we examine the impact that these changes have had on the mathematical education of students. Have students been thriving with the new standards and courses? And if so, what is the proof of this?
To Schlichter, the answer is yes–students have been thriving. Said Schlichter, “In LVJUSD, our math test scores are generally improving over the last three years and we scored higher than Alameda County and the State of California.”
But while our success in testing and as a district is important to recognize as part of the outcome of the new standards and courses, inside the classroom is where it really matters.
Teresa Hallum, who teaches sixth to eighth grade math at Joe Michell Elementary and Middle School, said, “I feel the changes were positive for students. Before the change, all students were in Algebra in 8th grade and many of them struggled. I feel that adding the Math 8 course helps students to better prepare for taking Algebra as freshmen in high school. Several of my students have come back to see me, and many of them feel they are better prepared and are more successful in Algebra 1 in high school.”
She added that, if eighth graders complete Algebra 1, they “are still on track to complete Calculus in high school….A student that takes Algebra in eighth grade will take Geometry as a freshman, Algebra 2 as a sophomore, Pre-Calculus as a junior, and Calculus as a senior.”
Hallum also mentioned that, since Joe Michell, being a small school, did not offer Geometry before these changes like other middle schools in the district did, they were not affected in that regard.
However, she continued on, saying that her daughters were juniors in Calculus, like so many who were given the opportunity to take Geometry as early as eighth grade. “Both of them ended up not having a math class as seniors,” she explained. “I feel they would have been better off taking Calculus as seniors, and not being pushed so fast through the curriculum in middle school.”
In short, Hallum declared, “I like the changes that were made. I feel our students have the chance to mature and are more developmentally ready to learn the abstract concepts in Algebra and Geometry.”
Rebecca Ahmadi, a Math 7, Accelerated Math 7, Math 8, and Algebra 1 teacher at East Avenue Middle School, shares a similar perspective.
Ahmadi believes that taking the pressure off students by having them not take Geometry, or even Algebra 1, until high school “is better for everyone in the long run. Students are more likely to learn math more deeply and be able to use and remember those concepts for a longer period of time. Recent brain research supports this change as it follows the typical brain growth of adolescents.”
Schlichter also shared her own experiences, saying that she took Algebra 1 her eighth grade year, and Geometry, Algebra 2, Pre-Calculus, and IB Calculus during her high school career.
“I did very well in high school…and passed the Calculus IB exam,” she said. “I retook Calculus in college because I thought it would be important for a solid foundation in Calculus and taking higher math courses later on, even though I tested out of the first semester of Calc in college. Calculus was harder in college than high school, even though I took the IB Calculus class. I am glad that I retook Calculus in college as it gave me an even deeper understanding.”
In order to better illustrate the significance of the changes in our district and state, Ahmadi described how the former structure in math standards and courses affected students. She stated, “Before CCSS, colleges were deeply concerned that many advanced students were coming out of high school with A’s in Calculus but then failing the colleges’ placement exams. Students were getting a lot of information and were able to spit it back in the short term but they weren’t holding on to those concepts or seeing the connections between them making application a lot more difficult.”
Ahmadi then went on to explain the impact of a differently-paced math curriculum on college admission and success. “This newer system allows more students access to even prestigious universities as excellence on the non-advanced path is still an open door,” she remarked, “whereas before if you didn’t get accelerated in math in middle school you missed your chance at Harvard, Stanford, or Cal.”
The California Content Standards for Mathematics from 2010, and the middle school math course changes that accompanied them, have evidently been instilled to solve the problem of a lack of in-depth teaching and understanding in fast-paced math classes, an issue I understand firsthand. But the students affected have not yet advanced through high school, let alone reached a point where the effect is reflected in their entrance into college math courses. That has yet to be seen. However, if they progress as our District Math Coach and teachers hope and believe they will, sacrificing a year or two of extra math classes may well be worth it.
Header credit: Kyla Giffin