The State of Connecticut has adopted the Common Core Curriculum Standards. As a result, the Fairfield School District has recently adopted the Common Core Curriculum Standards for Mathematics and has selected to use College Preparatory Mathematics (CPM) curricula, textbook and instructional method to align with the Common Core Standards for Mathematical Practice and Content.
The Common Core Curriculum Standards do not mandate a specific teaching methodology or instruction for mathematics; rather it is at the discretion of the school districts to decide on instruction.
College Preparatory Mathematics uses a teaching methodology called “complex instruction” which is based on “pure discovery” of problem-based tasks in study teams with “interrupted” practice on course concepts. This teaching methodology is used on a daily basis.
Parents and students have many concerns related to College Preparatory Mathematics (CPM):
- College Preparatory Mathematics (CPM) bases instruction on small group learning with only supplemental guidance from the teacher. The teacher’s role is to facilitate instruction as he/she circulates the classroom ensuring students are on task.
- The teacher instructs the whole class for a fraction of the class time: one-third of the class time at maximum
- The teacher is not allowed to “give away what the students are to discover on their own”, rather his/her role is to facilitate thinking through asking them to make predictions.
- The majority of class time is focused on students using self-directed group learning (cooperative learning groups) to teach new mathematical concepts to themselves and each other, as well as review concepts from previous chapters within their groups.
- Self-directed group learning emphasizes the importance of all students within the group mastering and understanding the concepts. Students are responsible for not only their own mastery but their peers’ mastery of concepts, as well.
- Memorization of formulas and skill practice are discouraged. Limited math problems for homework.
- Why should the social aspects of group learning inhibit one’s ability to learn math? CPM requires students to surmount any and all group social issues within the group dynamics, while simultaneously trying to solidify the understanding of mathematical material.
- How does this instructional method of cooperative group learning impact students with learning differences such as attention deficit disorder, dyslexia, non-verbal learning disabilities, and executive functioning disorders (estimated to be 15-20% of the student body)? What if this method is not working for these types of learners, are they allowed to opt-out of the group learning or required to “persevere”?
- How does the same level task engage different levels of learners within the mixed ability groups? For some students the mathematics may come easily, while others may be struggling to understand the concepts. Since there is no pre-assessment of prior knowledge of material before grouping students, working together in mixed ability groups has proven to be onerous and frustrating for all students to date. A student is not allowed to move ahead or accelerated until everyone in the group understands and has mastered a concept.
- How will these students perform on SAT, ACT and AP exams? To date, no independent studies or data have shown how students studying mathematics under CPM’s method of instruction perform on these standardized tests. The lack of information leaves parents and students apprehensive, as many colleges, particularly those with extremely competitive admissions, care a lot about scores. In addition, many colleges use test scores to award “merit aid” scholarships, which is financial aid not based on need.
- CPM places an overly enthusiastic emphasis on explaining math answers in written form. This method penalizes students who are strong in understanding mathematical concepts and formulas but weak in organizing thoughts and explanations in written expression. Strong math students are not always the best writers.
In summary, the instructional methods of College Preparatory Mathematics require students to discover new concepts in small group settings with minimal teacher instruction and lack of differentiated curricula.
Students have different learning styles, levels of abilities, and prior knowledge of mathematics, but our district believes that we should compact them into one size.
However… One Size Does Not Fit All.