Math in the Lower School: “Putting kids in the driver’s seat”

Math in the Lower School: “Putting kids in the driver’s seat”

Math in the Lower School: “Putting kids in the driver’s seat”

Teachers use strategies and tools to help students develop a strong conceptual understanding behind the number facts they learn and the many ways they apply them.

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 Lower School, teachers use a range of research-driven strategies and hands-on tools to help students develop a strong conceptual understanding behind the number facts they learn and the many ways they apply them. Along the way, they’re building strong communication and collaboration skills, making today’s math students more prepared than ever to jump into higher-level math and the many exciting opportunities it offers in the 21st-century world.

The building blocks: “Learn and extend primary math skills”

Ravens begin their mathematical journeys in PreK and kindergarten, learning to identify numerals, count, and understand cardinality and one-to-one correspondence. Teachers integrate these foundational concepts into everything they do in the classroom, from daily routines to learning centers.

PreK teacher Crystal Garris and teaching assistant Warsha Rao lead the class in a counting song about Herman the Worm that helps them identify numerals 1-10.

“In PreK, math skills are incorporated into activities through various play-based approaches. This allows us to provide fun, collaborative and creative ways for students to learn and extend primary math skills,” PreK teacher Crystal Garris explained. “Morning circle time allows students to engage in routines, such as calendar activities, that incorporate counting and identifying numbers. Learning centers include counting manipulatives, pattern blocks, math picture books, and puzzles and problem-solving activities. Brain Breaks are fun ways for students to move their bodies in a fun and interactive way.”

Kindergarteners build on that learning, solidifying their understanding of cardinal and ordinal numbers, counting to 100 by ones and 10s, adding and subtracting, comparing quantities, and composing and breaking down numbers using 10s and ones.

First page of the PDF file: ETHOSMIFMathTalk

These Math in Focus worksheets provide practice for students in Megan Britton’s kindergarten class learning about ordinal numbers through 10.

They also continue learning to subitize — to instantly recognize the number of objects (such as three lollipops or five pennies) without counting them, a skill that comes in handy as they are asked to combine quantities of numbers together. And the learning just continues from there.

“The development of foundational place-value understanding occurs in the lower grades and is built upon in the middle to upper elementary grades,” Assistant Head of Lower School for Student Learning Erin Cole ’04 explained. “Numbers and operations in Base 10, measurement and data, geometry, operations and algebraic thinking build across grade levels and allow for vertical alignment in learning.”

By the time students are in fifth grade, they’re burnishing skills in multiplication and division, understanding place value into decimals and performing operations with fractions. Along the way, they’ve developed the solid mathematical habits they will use for years to come: looking for patterns, strategically using tools, leaning on their understanding of mathematical models such as diagrams and symbols, and — most importantly — persevering in problem solving.

These anchor charts in Nicole Spivey’s fifth-grade math class remind students how to perform operations with fractions.

Approach “really forces them to think”

These mathematical concepts are likely familiar for many Ravenscroft parents and guardians. What’s likely less familiar is the approach being used to teach them. Just as the teaching of reading has been revolutionized by contemporary research, the approach to math instruction has shifted purposefully as well.

“If you ever heard of ‘mad minutes’ — testing how many multiplication problems students could solve in one minute — a lot of math instruction used to involve that kind of memorization. While there is a value to automaticity in mathematical competency, today’s approach is all about the ‘why’ and having a strong number sense,” Head of Lower School Nicole Girvan explained of the change. “You can’t do college math successfully unless you understand the ‘why.’”

Recognizing the need for an updated approach, in 2021 the Lower School adopted Math in Focus for K-5 instruction. (A complementary curriculum, Math Expressions, is used in PreK.) Using a progression across three modes of learning — concrete, pictorial and abstract — Math in Focus ensures that students don’t just rely on memorization and shortcuts. Rather, they come to understand the processes themselves.

Second-grade teacher Tegan Stanford, who is the Lower School math curriculum co-chair, illustrated how her class might consider equations using this approach.

“We’re used to seeing 2+2=4, but what if we said, ‘Could 2+4=7-5?’ It’s more about understanding that both sides of the equation are balanced. That’s very abstract, so to begin with we help them understand using cubes and actual scales,” she said. “A first-grade teacher might put two cubes plus four cubes on one side and seven cubes on the other, then take away five. ‘Is that balanced?’ ‘No, it’s not.’”

Students in first grade make use of a variety of hands-on tools, such as cubes and scales, as they learn early mathematical concepts; here, Ward Gibbons and Taylor Rouse connect cubes to complete an activity in Avera Sinnett’s class.

Stanford emphasized as well that, at every step of the learning process, students discuss what they’re thinking and learning with their peers. “It’s not just the teacher barking information,” she noted.

Fifth-grade math teacher Nicole Spivey, who is Stanford’s math curriculum co-chair, seconded this approach, which encourages students to pull from prior learning and try various tactics, often using their knowledge in new ways.

“Sometimes, to start a lesson, I give them a problem where I really don’t want the answer, I just want to know what they’re thinking. I let everyone share how they would solve it,” she said. “After the lesson, we’ll come back to it and see: ‘All those different strategies we talked about, will they work in solving this problem?’ That really forces them to think.”

“It’s all about putting kids in the driver’s seat,” Cole added.

Third-grade tools such as numbered dice support students as their mathematical understanding grows more complex; here, Leslie Hatcher’s students Aubrey Smith and Keyan Coole work on an activity introducing fractions.

Math in Focus has other strengths as well. The structure of the lessons allows teachers to do frequent assessments — both formal and informal — to gauge how students are progressing and adjust the pace as needed. The curriculum also supports differentiation.

“There are extra practice pages and enrichment activities in each chapter,” kindergarten teacher Megan Britton said. “I support students who need extra practice by pulling them into a small group to do a reteach lesson or meeting with them one-on-one.”

The Math in Focus student workbooks include extra practice worksheets to help students master important concepts.

The learning continuum also helps the division as a whole measure the progress of their young learners year over year.

“I can see what my second-graders learned in first grade and, if they still need to master a skill from before, we have access to all kinds of materials,” Stanford said. “And the longer we have this program, the more data points we’re going to have.”

Developing “the four C’s” and a growth mindset

The result is an understanding of math that is both broad and deep, evidenced in no small part by the many ways students successfully use math in other parts of their school days.

Third-graders working on their entrepreneurship unit calculate the cost of manufacturing an item for their market day. Fifth-graders weigh and tally the meals for their service project with Rise Against Hunger. Nascent musicians in general music, strings and band classes count out beats and play whole, half and quarter notes to precision so their duets, trios and quartets come together as one song.

Students use math in a variety of ways (clockwise from top left): a whole class counts beats together as they drum in Mary Royall Hight’s music class; kindergartener Ben Kennedy learns to bow in Tasi Matthews’ strings class; fifth-graders including Jeremy Shirak measure and weigh ingredients during their service project; Innovation Lab teacher Danny Carlson prepares fifth-graders for an activity using TinkerCad, which builds on their understanding of shapes and spatial relationships.

In the Lower School Innovation Lab, budding creators stretch and apply their skills in myriad ways.

“Mathematics is a thread that is woven through the entire fabric of the Lower School IDE experience,” Innovation Lab teacher Danny Carlson said. “In the younger grades, students practice spatial reasoning and awareness through building activities. This lays the groundwork for a more complete understanding of geometry concepts. Entry-level coding activities provide an introduction to grouping processes that eventually become the foundation for solving algebraic expressions. Coding also strengthens the understanding of sequence and order of operations. As our students begin two- and three-dimensional CAD design, they are given an opportunity to apply their knowledge of area, perimeter and volume to practical situations.”

Interestingly enough, math skills aren’t the only learning outcomes from students’ work in math. Along with that depth of knowledge come “the four C’s”: collaboration, communication, critical thinking and creativity — 21st-century skills every student needs.

“Students are going to approach the problem and come up with ways to solve it, then they’re going to talk about it. That ‘math talk’ gets them to think about the language they’re using,” Cole explained. “They’re agreeing or disagreeing or defending their argument.”

“We’re giving a child the opportunity to create their own word problems that their neighbor can then solve,” Stanford added. “There’s a math journal at the end of every chapter, so kids are writing about their thinking and supporting it with ideas, details, examples.”

Fifth-graders Sydney Westbrook and Evelyn Canavan collaborate on solving decimal problems during a math scavenger hunt in Mrs. Spivey’s class.

With the classroom transformed into a restaurant, Mrs. Spivey and fifth-graders Daniel Campos, Austin Short and Daniel O’Quinn review their knowledge of decimals to figure out the cost of a meal.

Most importantly, teachers work to cultivate a growth mindset — which is particularly important in a discipline that parents may remember as rigid and focused only on getting the correct answer.

“It’s the idea that they don’t have to have the right answer now,” Cole said. “There may not even be a ‘right’ answer, right? That idea that they can sit in that productive struggle and try multiple things before they arrive — that’s a life skill that I certainly wish I had more exposure to when I was in school.”

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