Math in the Middle School: Growing “more confident in their ability”

As one of the core academic disciplines — and with an ever-growing list of real-world applications — mathematics is at the heart of students’ experiences at Ravenscroft. Whether it’s being able to understand the concept of one-to-one correspondence when counting or the complex functions of multivariable calculus, students digging into math rise to the challenge and find satisfaction in success.

In the Middle School, teachers build the bridge between the Lower School’s development of solid number sense and the increasingly abstract disciplines of Upper School math, viewing math as a journey where students focus on a deeper, more conceptual understanding of the processes they’re learning. They’re supported in their work by an innovative approach to grading and a range of courses designed to provide the right amount of challenge as students grow and explore.

Math 6 student Lucy Shaw ’29 volunteers to share her ideas about solving a problem requiring the use of long division in Karen Ojeda-Watkins’ class.

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A bridge from Lower School to Upper School

As students transition from fifth grade to sixth grade, they find that the Middle School Math Department has been very intentional in crafting courses that build upon their skills — and their growth mindset — as they begin to explore new and increasingly abstract concepts.

“We look at the standards and concepts they’ve covered in Lower School and where we need to get them for algebra and, in some cases, geometry in ninth grade,” Math Department chair Erin Altshuler explained. “We have made the scope and sequence of our courses to align with that.”

The teacher-designed curriculum begins with Math 6, a course that solidifies concepts learned in Lower School, such as fractions and decimals, and explores exponents and order of operations. Math 7 introduces integers, solving equations and inequalities, and proportional reasoning. In Pre-Algebra, teachers lay the groundwork for Algebra I by exploring variables, rules of exponents, integers, solving and writing equations and inequalities, and rational numbers.

Karen Ojeda-Watkins’ Math 6 students show their thinking as well as their results in this exercise on adding fractions and mixed numbers.

In this warm-up exercise, Lindsey McKearney’s Math 7 students are challenged to use the digits 1 through 9 at most one time each to fill in the boxes to make a true statement.

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One significant difference from the approach in Lower School: the department offers differentiation through separate course curricula beginning in sixth grade, with about 50% of students typically enrolling in Math 6 — designed to ensure students have a deep understanding of foundational concepts — and 50% taking Advanced Math 7, which positions students to take Algebra in eighth grade and Geometry in ninth.

From Math 7 on, courses are offered at both a standard level (known informally as “college-prep” or “CP”) and at an advanced level. The primary differences are the pacing of material, the depth of information covered and the degree to which students work independently.

“CP classes are going to be smaller because we want to make sure students get individualized attention and really develop strong knowledge of the subject,” Altshuler, who teaches Algebra and Advanced Pre-Algebra, said. “In advanced classes, we expect students will advocate for themselves and know how to get help if they need it.”

There are two additional hallmarks of the Middle School math curriculum, both designed to ensure students are set up for success: required practice exercises over the summer, based on the course students are taking in the fall; and Math Lab, an optional curricular support session Altshuler offers several times a week during recess and tutorial periods.

Math Department chair Erin Altshuler, shown here teaching an Algebra class, also offers Math Lab multiple times per week, providing students in all courses extra support and practice.

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“Math Lab not only helps strengthen students’ math skills, but it also gives them the confidence they need,” Karen Ojeda-Watkins, who teaches Math 6, said. “As a teacher, it is rewarding to see the growth that a student shows, both on paper and in their attitude toward math, after they attend Math Lab regularly. Their investment in the course also increases through participation and quality of work.

“Math Lab shatters a common misconception — students may think that they aren’t good at math because they can’t do quick mental math or absorb conceptual understandings after just one class,” she added. “Math is the universal language everyone can do, even if more practice is required for a student to master a concept! Math Lab gives our students the avenue to do so.”

New approaches “respond to student need”

As in the Lower School, teachers have shifted to an instructional approach that favors a deeper, more conceptual understanding of mathematical principles.

“The Middle School math teachers all have a similar philosophy: math is a story, a journey,” Pre-Algebra and Advanced Algebra teacher Shayla Coleman said. “My job isn’t to tell you how to do all of the problems, because then you don’t make the connections. You just see it as steps to do, versus focusing on the understanding of why: ‘Why do we solve an equation this way?’ I think you’ll hear all of us asking questions instead of focusing on the rote process.”

Middle School makes use of math journals, where students keep handouts, worksheets and their own notes on what they’re learning in class; at left, a page from Erin Altshuler’s master journal for Advanced Pre-Algebra; at right, a student flips through her own journal during a lesson.

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As part of that approach, the department has adopted an assessment tool that provides students with meaningful feedback. Using a rubric with a scale from 0 to 5, teachers give students important context about their grade — whether, for example, they lost points on a problem due to a minor computational error or a conceptual misunderstanding.

“You used to do the calculations, spit out the answer and either get it right or wrong,” Altshuler said. “We also look at their process, and we grade based on learning targets.”

Colleagues said use of the rubric has been a game-changer.

“No longer does a student receive an assessment back and only see a score of 90%,” Math 7 teacher Lindsey McKearney said. “I often tell students to ignore that average at first and pay attention to the individual 0-5 score, which puts them in a better position to understand their grade. This also normalizes talking about errors, that making them is part of the learning process.”

“Their being able to self-assess and our knowing what they mean — ‘I’m a 5, I really have that concept’ — has really helped. As they move from teacher to teacher, that common language helps us identify their places of growth,” Coleman added.

The department provides more detailed and actionable feedback about students’ work on assessments using this rubric, providing what teacher Shayla Coleman calls “a common language” across all math courses.

New “on- and off-ramps” between CP and advanced courses give students more opportunities to find the appropriate level of challenge as they make developmental leaps in Middle School.

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Another change, put into place last spring, creates additional opportunities — known as “on- and off-ramps” between CP and advanced courses — for students to find the right level of challenge. It’s predicated on an awareness of what Altshuler calls the “huge, huge developmental changes” students experience as they move through Middle School math.

“Previously, if a student took Pre-Algebra as a seventh-grader and was not going to be successful in Algebra, their only option was to retake Pre-Algebra,” she explained. “Saying they’re not going to be successful in an eighth-grade algebra course is not saying they’re not ready to do algebra — it’s saying they might need a slower pace or things broken down more. We realized that we were not opening doors for students who were hitting their mathematical strides after fifth grade.

“We really responded to student need when we made this change.”

Simran Vishnubhakta ’27 and Kayla Hu ’27 tackle exercises on function notation during Shayla Coleman’s Advanced Algebra class.

Shayla Coleman checks in with Luke Davis ’27 and Cavan Sheehan ’27 as they practice a new skill in Advanced Algebra.

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The shift supports students wanting more challenge as well. As part of the rubric-based assessment, students can opt to do problems that require an extension of their learning or a new combination of skills — letting them show their teachers that they’re willing to take risks and put in the work required in advanced courses.

“I think the new approach has been great,” Advanced Math 7 and Pre-Algebra teacher Brian Stumm said. “It provides a path for students to be appropriately challenged, rather than bored or frustrated, in math.”

Finding value in “experiences of productive struggle”

The overarching goal of the department, of course, is to prepare their students for higher-level math — which can include challenges outside the curriculum itself.

“The space for frustration and ambiguity is a major part of high school math,” Altshuler acknowledged. “Understanding how to persevere is essential. Middle School math is working to build in those experiences of productive struggle — showing students the payoff that comes when you keep pushing through.”

“I am hopeful that students grow more confident in their ability to jump right into new material, because struggling and finding ways to work their way out of it is important,” McKearney said. “I often tell my students to ‘be comfortable with being uncomfortable’ as they go through their mathematical journey. These behaviors will allow them to be more successful as they move into the next level.”

Middle Schoolers have additional opportunities to explore the benefits of creative problem solving and perseverance, thanks in part to a robust slate of electives that help students discover real-world applications of their hard-won skills.

Michelle Nunalee’s Engineering I students, for example, learn Ohm’s law (voltage=current x resistance) and graph data gathered from test blades as they work to design efficient turbine blades for the online KidWind competition. Engineering II students use math in building model homes powered by solar panels.

“The students calculate the efficiency of our classroom solar panels and compare the efficiency to commercial solar panels. We collect illumination and energy data using Vernier light and energy sensors and then calculate averages of multiple trials,” Nunalee explained. “Students also get practice working with unit conversions so they can accurately compare the energy output of the sun to the energy output of the solar panels when they calculate efficiency.”

Middle School Engineering students Mila Sharkady ’28 and Anna-Belle Shaw ’28 calculate the efficiency of the solar panels they are using on their model solar home.

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The popularity of these electives is just one indication that the Math Department’s approach is resonating with students. Of course, the teachers see it in their own classes, too.

“I think it’s also their excitement when they’re presented with new material,” Coleman said. “And they do get excited to learn something new. They get excited to build on something they already know how to do. They even get excited about talking about why we’re doing what we’re doing.

“I know they’re on the right track when I say, ‘Let’s do a few examples together,’ and they’re like, ‘Nope, we want to do it, and we’ll check in with you if we have a question.’ That’s how I know we’re in a good place.”

Want to learn more? Read about math instruction in the Lower School and in the Upper School.

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