Menlo’s math department values depth over speed, conceptual understanding over memorization, and kindness over competition.
We aim to create opportunities to build skills that enable our students to become problem solvers and not just calculators. Throughout students’ middle school years, they are expected to not only solve problems but also reason abstractly, demonstrate multiple problem-solving strategies, make connections between mathematical concepts, and to justify and communicate the process they went through to solve the problem.
“Education is not just the learning of facts but the training of the mind to think.”
—Albert Einstein
Our Curriculum
At Menlo Middle School, our curriculum focuses on relevant, engaging, and challenging tasks where students will experience math in ways that promote a deep understanding of mathematical concepts. As part of our innovative program, we are consistently reconsidering the importance and effectiveness of traditional classroom methods. As teachers, we aim to have students actively thinking as much as possible, moving away from the role of instructor to one of facilitator and curator or engagement opportunities. Versatile problem-solvers cannot be molded and supported properly with traditional teacher-led instruction that focuses on memorization and repetition. Deep conceptual understanding is required to create a skilled problem solver. This must all happen in addition to memorization and practice. Any memorization or repetitive practice should only come after the students have had the opportunity to explore, make connections, and try to develop an understanding of the how and why.
Thoughts on Leveling
Students’ brain development and cognitive ability mature at different rates. With this in mind, we do not level 6th grade math classes. This allows for the teacher to be able to observe the student for themself and then decide, based on Menlo’s curriculum, which level will benefit them most in 7th-grade. In 7th grade, there is one section of enriched math and 3 grade-level classes. We have found that only ¼ of the students are typically ready for the added depth of knowledge that the enriched curriculum requires. Once in 8th grade, half of the students are placed in enriched classes and half in grade-level classes, as by their 8th grade year, more students are ready for the enriched curriculum.
Topics studied include those listed in Algebra 8. In addition, students are further challenged to investigate connections between concepts and pushed towards deeper understanding and flexibility in problem-solving, through more rigorous applications. Students are also introduced to the idea of a mathematical proof.
Grade: 8
Algebra 8
This Algebra 1 course prepares students for the rigors of future classes by providing a strong foundation of algebraic concepts. Students will explore multiple representations of the linear, quadratic, and rational functions. Extensive treatment of the fundamental skills that underpin various relationships precedes the study of these functions. Real-life applications will be explored whenever possible. Additional topics covered include a review of operations with integers and rational numbers, solving equations and inequalities, operations on polynomials, radicals and rational expressions, factoring, functions and graphs, linear systems, and quadratics.
Students practice cooperative problem solving and learn effective communication skills that use the appropriate mathematical language to present problem solutions.
Grade: 6
Mathematics 6
The goal of this course is to create a solid foundation in mathematics that students will need and use in the years ahead. Emphasis is on strengthening computation skills, especially those involving fractions, decimals, and integers, and developing a thorough approach to problem-solving. Students will be challenged daily to develop mathematical habits of mind such as making sense of problems, utilizing appropriate solution strategies, communicating their methods with mathematical justification, and persevering through challenges. Organization of thinking and documentation of work are strongly emphasized. This course is designed to meet the needs of students with a variety of math backgrounds and provide challenge and engagement at all levels.
Topics covered include number theory, problem-solving, proportional reasoning, integer operations, data and statistics, probability, and geometry. The use of variables is woven throughout the curriculum to help prepare students for pre-Algebra.
By the end of 6th grade, students should feel confident in their abilities to reason through complex problems and be comfortable working with variables.
Grade: 7
Pre-Algebra (E) 7
Topics studied include those listed in Pre-Algebra 7. In addition, students are further challenged to investigate connections between concepts and pushed towards deeper understanding and flexibility in problem-solving, through more rigorous applications.
Grade: 7
Pre-Algebra 7
This Pre-Algebra course provides students the opportunity to stretch their abstract thinking, critical thinking, and analytical reasoning. Students will continue to work on documenting in organized steps and sharing verbally their thinking and solution strategy. In addition, they will learn to defend their methods in peer review. In this course students will be presented with challenging but accessible problems, and asked to reason through them collaboratively with their peers.
Students will be introduced to formal algebraic thinking and apply algebraic concepts to their prior problem-solving strategies. Other topics include exponents, geometry (angle relationships, surface area and volume of 3D shapes), scale, ratios, proportions, percents, statistics, and probability.
Frequently Asked Questions
We have also collaborated with the Upper School in ensuring that regardless of the classes a student takes in grades 6-9, if the student is ready to challenge themself, there are pathways to all advanced and honors classes in the Upper School.
We don’t offer any compacted or accelerated math courses at Menlo Middle School. We level students once they are in 7th grade, but instead of challenging them by introducing new concepts, we add rigor to the curriculum by asking students to explore concepts in more depth. We achieve this depth by engaging students in lessons and situations that require flexibility in their problem-solving, the use of multiple strategies, making connections to other concepts, and explaining why something works.
We believe that adding new concepts to create rigor has great potential to leave a student’s depth of knowledge more shallow than is needed of a student hoping to take advanced math courses in the Upper School. In addition, accelerating students into new concepts leaves other students behind. In many cases, these students will become “tracked,” meaning they will never catch up. This would have all taken place before they have had the time to mature into their true academic selves.
When students have already studied a topic that we teach, often they’ve learned this concept in an accelerated or compacted manner. This often takes place online and independently. These methods of learning tend to emphasize memorization and mimicry because of the design to move quickly without collaboration opportunities, explorations, or investigations. We believe that when students attempt to learn quickly without peers or a skilled facilitator it often leads to a lack of depth conceptually. At Menlo, students explore topics from a more organic nature. They reason through problems with their peers and teachers facilitate student learning by asking questions and redirecting to preserve one’s self-discovery. This process of learning is much more interactive and fun, and consequently, more sticky because it is memorable. Once students have explored, investigated, and collaborated, we then talk about algorithms, rules, and shortcuts and, importantly, why they work. Students’ conceptual understanding will be deepened by reasoning abstractly, developing multiple strategies, making connections to other mathematical concepts, and proving algorithms, all while communicating their understanding verbally and in writing. We believe that the depth of understanding a student gains from these collaborative investigations is vital to their future success in the advanced math classes they will take in high school.
Placement isn’t something that we rely solely on test scores on grades to determine. While a student’s academic achievements are key contributing factors to placement, we give strong consideration to a student’s versatility as a problem-solver, ability to articulate their thoughts, and soft skills like collaboration and organization.
Enriched and grade-level classes cover the same concepts. The difference is that students in the enriched class, generally speaking, have deeper conceptual understanding and are more versatile problem-solvers. Because of this, these students are further challenged to investigate connections between concepts and pushed towards deeper understanding and flexibility in problem-solving, through more rigorous applications and expanded exploration.
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