News Detail
Math for Deeper, More Enduring Understanding
Justin-Siena is initiating a new approach to student learning in Algebra I, Geometry/Honors Geometry, and Algebra.
We are excited about the new curriculum and instructional approach which have been proven in research to improve math fluency among students, develop stronger problem-solving and reasoning skills, build a stronger foundation for advanced mathematical studies, and prepare students in the types of mathematical skills that will be assessed on the new SAT (being implemented in March 2016). Many top schools such as Phillips Exeter have taught math with similar methods for over 20 years, and the methodology is supported by scientific research in learning and memory retrieval like that of Brown, Roediger, and McDaniel (2014), in their book Make It Stick: The Science of Successful Learning—recommended reading for all parents and teachers.
What’s the approach? How is it different?
Starting this year, our lower division math classes are taking a problem-based or problem-solving approach, which the National Council of Teachers of Mathematics (NCTM, 2010) defined as, “Mathematical tasks that have the potential to provide intellectual challenges that can enhance students’ mathematical development. Such tasks—that is, problems—can promote students’ conceptual understanding, foster their ability to reason and communicate mathematically, and capture their interests and curiosity.” The content of the Algebra I, Geometry, Honors Geometry, and Algebra II courses remain the same, but how the content is organized, practiced, and learned is different. The approach is based on NCTM procedural standards and prioritizes:
The value of this kind of intellectual struggle is supported by brain research. According to Brown, Roediger, and McDaniel (2014), effortful struggle, solving problems before being taught a solution, spacing out practice and application of previously learned skills—a method called interleaving (rather than massed practice or drilling all at once), and distilling underlying principles and rules contribute to deep, long-term learning that helps students retrieve content and skills and apply them in new settings and experiences in the future.
Geary, K. & Atif, S. (2013). Harkness Math. Independent Teacher. Retrieved from http://www.nais.org.
NCTM. (2010). Why is teaching with problem solving important to student learning? Retrieved from http://www.nctm.org
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What’s the approach? How is it different?
Starting this year, our lower division math classes are taking a problem-based or problem-solving approach, which the National Council of Teachers of Mathematics (NCTM, 2010) defined as, “Mathematical tasks that have the potential to provide intellectual challenges that can enhance students’ mathematical development. Such tasks—that is, problems—can promote students’ conceptual understanding, foster their ability to reason and communicate mathematically, and capture their interests and curiosity.” The content of the Algebra I, Geometry, Honors Geometry, and Algebra II courses remain the same, but how the content is organized, practiced, and learned is different. The approach is based on NCTM procedural standards and prioritizes:
- Student engagement in problem-based lessons structured around a core idea,
- Guidance by a knowledgeable teacher,
- Student interaction in groups to foster mathematical discourse, and
- Practice with concepts and procedures spaced over time so that mastery comes over time.
In the past, most math classes were dedicated to teacher delivery of content, topics, and skills to students. Teachers did most of the reasoning and thinking, while students worked mostly individually to engage in repetitive drilling or “massed” practice (Brown, Roediger, & McDaniel, 2014), which brain research shows is one of the least effective ways to learn content and skills so they can be retrieved and applied later.
With the new approach and curriculum, most time in math classes is devoted to students working in groups to problem-solve through discussion and discourse about realistic and relevant problems. The problems require higher-level thinking, use of multiple mathematical processes, consideration of various solution strategies, and justification of reasoning. In this model, the teacher serves as a “guide on the side” who actively encourages students to wrestle with important ideas and asking leading questions to help students establish connections among procedures, skills, and context (NCTM, 2007, 2010). In this manner, learning of mathematical concepts and procedures takes place as students attempt to solve and discuss problems “in which relevant mathematics concepts and skills are embedded (NCTM, 2010).
Isn’t this harder and more complex?
Yes, it is. And that’s a good thing! According to Mathematics Department Chair, Garry Carpenter,
Yes, it is. And that’s a good thing! According to Mathematics Department Chair, Garry Carpenter,
"Some students will find math class this year to be an unfamiliar experience. Students accustomed to lecture and note-taking will find less of those and much more of mathematical discussion and exploration. Students who have previously made it through math class without saying a word will find that they are talking about math continually with their groups. Students who succeeded just fine “the old way” will find that their understanding of concepts and connections is much deeper than ever before. And students who are afraid that “struggle” means “fail” will find that most things worth having are those that don’t come easily. We expect that some students will be uncomfortable at first, and we as teachers will be by their sides to help them as they learn to navigate the mathematics.
The value of this kind of intellectual struggle is supported by brain research. According to Brown, Roediger, and McDaniel (2014), effortful struggle, solving problems before being taught a solution, spacing out practice and application of previously learned skills—a method called interleaving (rather than massed practice or drilling all at once), and distilling underlying principles and rules contribute to deep, long-term learning that helps students retrieve content and skills and apply them in new settings and experiences in the future.
How will this new approach prepare students for college and life?
NCTM research (2007) has found that students who learned math concepts through a problem-based approach were better able to adapt their skills to solve new kinds of problems than students who learned math through direct delivery of content and skills by a teacher. Thus, students will be better prepared to apply their understanding in advanced mathematical subjects such as statistics and calculus and in applications in science, engineering, and computer science.
Furthermore, the new SAT, which current freshmen, sophomores, and juniors will take, will assess the kinds of skills being learned and practiced in Justin-Siena math classes: Conceptual understanding through which students connect equations and operations to different contexts; real world applications in which students analyze a scenario, represent the problem mathematically, and carry out a solution; and calculator use in which students discern how and when (or if) it is better to use a calculator or to apply their own reasoning in solving a problem. For more information on the math portion of the new SAT, click here.
The Justin-Siena Math Department is implementing this new approach to math education through research, training, and professional collaboration. Together, they are guiding our students to greater mathematical understanding and competence so that students are prepared for advanced mathematical skills and coursework. We are excited about the Math Department’s leadership in curriculum development and the deeper learning and relevant applications that will emerge from this new approach.
Free downloadable parent guides for the CPM curriculum:
- TED Talk: Three Rules to Spark Learning by Ramsey Musallam
Dr. Musallam teaches science at Sacred Heart Cathedral, another Lasallian school in San Francisco. His approach to teaching and learning correlate to the approach taken in Justin-Siena math classes.
References:
Brown, P.C., Roediger, H. L., & McDaniel, M.A. (2014). Make it stick: The science of successful learning. Cambridge, MA: Belknap Press of Harvard University Press
Geary, K. & Atif, S. (2013). Harkness Math. Independent Teacher. Retrieved from http://www.nais.org.
NCTM. (2007). Effective teaching for the development of skill and conceptual understanding of number: What is most effective? Retrieved from http://www.nctm.org
NCTM. (2010). Why is teaching with problem solving important to student learning? Retrieved from http://www.nctm.org
NCTM. (2014). What does research tell us about fostering algebraic reasoning in school algebra? Retrieved from http://www.nctm.org
Phillips Exeter Academy. (2015). Mathematics. Retrieved from http://www.exeter.edu
Justin-Siena High School
Justin-Siena is a Lasallian Catholic college preparatory community that serves young people in grades 9–12.