Problem Solving and the Common Core

Rationale

As our district transitions away from the traditional Algebra 1 – Geometry – Algebra 2 foundational mathematics sequence towards an integrated curricular pathway based upon the Common Core State Standards (CCSS),³ there are a variety of challenges in my mathematics classroom. In the first year of implementation of a new Common Core State Standards Integrated Math Curriculum (CCIM-1), I experienced more students struggling to adapt to an increased expectation of active engagement, discussion, and questioning in the mathematics classroom. A primary struggle by students with the new curriculum, the Mathematics Vision Project (MVP) Integrated 1 Curriculum,⁴ was the inaccessibility of text heavy scenarios and the expectations of student participation in order to drive thought and discussion that would help develop, solidify, and practice students’ mathematical understanding. Many of my students were unable to connect or relate to the contextual scenarios that framed each module in the curriculum. As a result of being unable to visualize and comprehend each fictitious scenario, student access to the mathematical concepts, intuitions, and learning objectives were significantly inhibited. Students were unable to connect with the MVP text heavy situational problems and tasks that were meant to elicit mathematical reasoning.

Most students entering the Integrated Math 1 course will have taken a Common Core Middle School Grade 8 course the previous year. However, the courses they are coming from have various course titles, utilize multiple different curricula, and students most likely have not received a full multi-year curriculum experience with Common Core aligned instruction. The CCSS Integrated Math 1 course is the lowest mathematics course offered to students in my district, and freshmen are defaulted into the course regardless of failing their prior course.

Last year, I team taught two sections of the CCSS Integrated Math 1 course with a special education co-teacher. The goal of the teaming was to provide opportunities for students designated as special education to be mainstreamed into general education classrooms. Both my co-teacher and I shared all classroom responsibilities including instruction, circulation amongst students, and assigning course grades. The student population in the team-taught class included approximately 25% of students with Individualized Educational Plans (IEPs) who were mainstreamed into general education classes. Approximately one third of students, coming from both general and special education, had reading levels far below grade level and were enrolled in corrective reading courses, and many were English Language Learners as well. Additionally, approximately one third of the students were identified as higher risk for not succeeding by their middle schools and were in a study skills class that provided social and emotional instruction in addition to academic support. Even though I will be team teaching, the materials designed for this unit are intended to be adaptable to any classroom.

Background and Demographics

William C. Overfelt High School is located in the heart of the East Side in San José, California. Overfelt’s notorious and generally negative reputation with the general public is inherited from a past where gangs, low academic achievement rates, neighborhood safety, minority population, and high proportion of low socioeconomic status households were dominant features. The disparity is only magnified by the school’s close proximity to the Silicon Valley. Approximately 80% of the student population identifies as Hispanic or Latino and approximately 90% of students qualify for Federal Free or Reduced Lunch.⁵

Currently, Overfelt is undergoing a transformation as the students, faculty, and community continually maintain a strong familial environment at our school campus that strives to emphasize a college going culture through challenging academic expectations, building student involvement through empowerment, and creating a safe space where everyone feels at home when at school. In recent years, the school culture and student academic accomplishments are in strong contrast to the perceptions and stereotypes that once defined the school. Overfelt has produced the most Latino high school student graduates and one of the highest proportion of Latino graduates out of any school in the East Side Union High School District.

One measure of the evolution of Overfelt can be viewed through the mathematics course offerings. When I started teaching at Overfelt six years ago, there was only one class section of Advanced Placement (AP) Calculus AB students. In recent years, approximately four times the number of students have been enrolled in AP mathematics courses each year, including Calculus AB, Calculus BC and Statistics. Despite gains in enrollment in higher level mathematics courses, there has been limited success for students who reach the courses. Furthermore, a far greater number of students are not succeeding in the foundational mathematics courses. Success in mathematics is elusive for a large proportion of students at Overfelt at all levels, but particularly in the freshmen entry-level integrated math course. Heterogeneous assignment of students entering the CCSS Math 1 course can result in classrooms with wide ranges of student prior knowledge, abilities in computational fluency, and attitudes towards mathematics. Students who did not succeed in middle school mathematics courses struggled immensely in my class with the new curriculum. In its first year of implementation, the percentage of students successfully completing Integrated Math 1 with a C or higher in my classes was below 40%.

To adapt to the curricular shifts due to the adoption of the Common Core State Standards, Overfelt refined its long term 5-year school vision. This curriculum unit is designed with Overfelt’s three primary instructional goals: (1) Implement student centered instruction that aligns to the common core and develops our graduate outcomes, (2) 25% of instructional time is teacher–led and 75% of instructional time is student-centered and spent on student exploration. (3) Assignments are “loose,” allowing students to build upon directions and create unique products to show learning. The goal is to have all students graduate with the critical and creating thinking skills as well as the resilience to succeed in college and careers. Simply stated, we want our students to have the option to get to and through college and/or thrive in their careers.