Mathematics

Problem Solving and Solving Problems.

Our goal as a mathematics department is to foster an ongoing interest in the study of mathematics and the skills it engenders, with as much consideration as possible for the different learning styles and needs of the individual student. We recognize that students in today’s world need to be able to work collaboratively, synthesize information, analyze, spot connections between topics, and problem solve. In particular, our goal is to create students who take great joy in applying their skills in a logical and methodical way to complex and unfamiliar problems.

Sequence

The vast majority of incoming students will start in the regular (non honors) ninth grade math program—whether that is in Analytic Geometry & Algebra or Integrated Geometry & Algebra with the summer Geometry component—and will be on track to take AP Calculus in the 12th grade. Our sequence goes from those freshmen courses to Algebra 2 in the 10th grade; Functions, Statistics & Trigonometry or Pre-Calculus in the 11th; and Pre-Calculus, Statistics or Calculus (AP or non-AP) in the 12th grade. You can view a flow chart of the math sequence possibilities here. Often, families seek to accelerate their child through our math program. However, in our experience, skipping classes or seeking placement in honors when this is not indicated by our placement process and teacher recommendation is rarely a good idea and ultimately may do nothing but damage to a child’s self-esteem and confidence. Going faster is not going smarter in most cases, because concepts are often ill formed or poorly understood. Students need to build a skill set in proper sequence at an appropriate pace in order for them to learn most effectively.

Placement Issues

Math placement is not an exact science, and no placement test ever gives enough information about how kids will thrive in our environment. The truth is that the vast majority of incoming students arrive with an A average in math, and we find ourselves having to tell students that while an A grade might reward due diligence at a lower level, it is only an indicator rather than a guarantee of success at higher levels. In the Upper School, we offer several different math classes, with fewer different levels in the lower grades and more for juniors and seniors. As our program is both challenging and inevitably quite different from the varied programs we see at our numerous feeder schools, our approach is to work with all our students in our core program for their first two years of high school before offering many different levels of classes.

The Honors Program

Students who are quite insightful in math will be placed in our honors program. The honors track is extremely rigorous and fast paced and is designed for mathematical enthusiasts. Honors Analytic Geometry & Algebra meets the needs of students who typically are able to understand new concepts in their math courses quickly and are yearning to go into more depth with just about every math topic that they meet. These students will develop their abstract thinking skills and will find plenty of challenge among their like-minded peers. Students who stay in our honors track go from Honors Analytic Geometry & Algebra to Honors Algebra 2 sophomore year to Honor Pre-Calculus in junior year to AP Calculus BC in senior year. Students in AP Calculus BC are also allowed to concurrently enroll in our highest math class, Advanced Topics in Math.

FAQs and Freshman Information

How do you determine which math class my child is placed in at the beginning of his Freshman Year?
Placement in math courses is based on three pieces of information: (1) standardized test scores; (2) teacher recommendations; and (3) performance on our placement exam. At the Welcoming Event in late April, every student will take a Placement Test to determine which math course they are best suited for. We believe in appropriately challenging students and do our best to place students in the best class for them. However, because the process is not perfect, during the first few weeks of school, freshmen teachers are very vigilant about determining if their students have been appropriately placed. Thus, inevitably there are a few changes that happen early on in the school year.

What is Menlo’s honors program in mathematics like?
Our honors program is designed for those students who are mathematics enthusiasts and are developmentally ready to delve deep into math concepts. Not only is the pace faster in these courses, but also every day students are expected to apply their knowledge to unfamiliar situations. In addition, honors students must be able to think flexibly across different strands of math, often picking and choosing from among a variety of mathematical tools in pursuit of a solution. Teachers of these courses usually serve as coaches, guiding the students along and offering help as needed, while the students work collaboratively during class to tackle challenging problems. As in our other courses, our honors students also are expected to display their work in a logical, organized manner.

My child has already taken Algebra and Geometry at her middle school. Does she have to take your Analytic Geometry & Algebra course?
Virtually all freshmen will start off in our Analytic Geometry & Algebra course. We recognize that many middle school students have had courses involving algebra and geometry. However, our course, and our program as a whole, is different from and substantially more challenging than courses at area middle schools. We believe in the importance of strong foundational skills, but more importantly our program emphasizes applying those skills to problem solving, synthesizing material, analyzing situations, working collaboratively, and moving flexibly between topics in mathematics. For those students who are still developing a solid foundation of algebra skills, we recommend taking our Integrated Geometry & Algebra course. For those who are ready to make the leap to problem solving with their algebraic and geometry knowledge, we believe Analytic Geometry & Algebra is the perfect course for them.

If my child does not start off in the honors track, can he/she move into that track down the road?
Yes, every year we have a few students who move into the honors track from the regular one. In order for this to happen, the student needs both to receive a strong recommendation from his/her previous math teacher at Menlo as well as to perform well on an honors placement test. In addition, usually some extra summer work is required.

If my child is not in the honors track, can she still take Calculus?
Yes! In fact, our top students in our non-honors track take AP Calculus AB as seniors. There also is the opportunity to take our non-AP Calculus course for those students not yet ready for the rigors of a college-level calculus course.

What is Integrated Geometry & Algebra?
We believe that strong algebra skills are the foundation of success both in our academic program here at Menlo as well as in advanced study. Mathematical development in students, like physical development, is a fits and spurts process. Some students arrive to Menlo with holes and weaknesses in their algebra knowledge that will prove problematic in future math and science classes. Integrated Geometry & Algebra is a course designed to develop strong foundational algebra skills that students can build upon. This course includes not only algebra, but also arithmetic/mental math skills and problem solving experience. In addition, beginning in the second quarter, the curriculum is integrated with geometry. Unlike most middle school Algebra I and Geometry courses, in Integrated Geometry & Algebra there will be a strong focus on learning the material on a deeper conceptual level and applying it to the freshman Physics curriculum. We want students to move beyond basic procedural competence to develop a strong understanding of material. In conjunction with the algebra and geometry topics, students will learn how to document their work and how to study effectively for assessments in mathematics.

If my child starts out in Integrated Geometry & Algebra, does that mean he always will be a year behind his peers?
Because we as a department and school are very sensitive to the potential social and confidence ramifications of a student being a year behind his/her peers in a particular subject, we view Integrated Geometry & Algebra as a 10 ½ month course for those students who are ready to make the leap to Algebra 2 as sophomores.  Thus, for those students who excel in Integrated Geometry & Algebra and wish to catch up with their peers after Freshmen Year, we offer a three-week summer intensive Geometry course. If a student successfully completes this course, he/she can start in Algebra 2 Sophomore Year with his/her peers. Students who do not take the summer component of the course would take Analytic Geometry & Algebra as a sophomore.

My child really wants to be able to take all of your math courses, including AP Statistics and Advanced Topics. Is that possible if they start out in your Honors Analytic Geometry & Algebra class?
For those students who remain in our Honors Program, they have the opportunity to take AP Statistics concurrently with either Honors Pre-Calculus or AP Calculus. In addition, students can, and many do, take both AP Calculus BC concurrently with Advanced Topics during their Senior Year.

AP Statistics also can be taken by those students who successfully complete Analytic Pre-Calculus.