A Customized Approach to Math

A Customized Approach to Math

Tuesday, January 19, 2016 - 12:00am
Written by  Jamie Baker

Adapting to the Learner + Adjusting the Curriculum

A changing world creates design opportunities for the smart and flexible school like PDS. “Historically, learning is one size fits all, yet classrooms have very diverse learners. Some students master concepts and skills relatively quickly and are rarely challenged, while other students need extra direct instruction and practice time on various skills and concepts,” says PDS Headmaster Lee Burns. “Smart schools are designing learning environments that adapt or adjust the curriculum on a daily basis to the needs of each learner rather than the learner being expected to plow through a set curriculum at a set pace.”


PDS 5th-grade math teacher Windy May put it this way, “If one of my students has already mastered order of operations, why should his class time be wasted on that when he is ready for a more advanced concept that day?”

Two summers ago, Mrs. May began working with Assistant Headmaster for Teaching and Learning Susan Droke and Chief Information Officer Cathy Kyle to develop a customized approach to teaching math for PDS. They collectively invested thousands of hours to design and implement an adaptive approach that allows for guided yet customized math learning journeys for PDS boys. In 2011-2012, May piloted the 5th grade approach they were developing in her classroom, improving the approach iteratively.

The goal for each boy’s quest is to achieve learning mastery so that he has a secure and lasting foundation for higher concepts and math reasoning to be layered upon.

“It's scary for a teacher to discard a very traditional, safe, standard-sized curriculum, but we knew that we could provide a better learning experience for boys by designing learning for the individual. It's a huge, exciting challenge and an opportunity to design and implement a customized approach,” says Melissa Smith, PDS Technology Coordinator for Virtual and Adaptive Learning.

To add to the project research, team administrators visited Stanford University and traveled to several reputable and innovative schools in New York and Silicon Valley to meet with educational leaders, teachers, and students about their adaptive curriculum and learning environments. The learning atmosphere they witnessed was so full of high levels of engagement, student ownership, problem solving, and great learning outcomes, their belief that a customized learning approach for each boy at PDS was the best approach for learning was confirmed.

In designing this customized program, each component skill that PDS 5th grade students needed to learn was mapped and sequenced. Mrs. May and the development team reviewed and curated hundreds of different math activities related to the different skills. They selected the best or designed their own activities for each skill. Recognizing that many boys would progress well beyond what is typically taught in 5th grade math, they also mapped and sequenced many more advanced math concepts and skills, creating a range of activities and projects to keep boys challenged and growing. Understanding that boys learn in different ways, they designed a variety of different approaches for each skill that incorporated the spectrum of learning pathways.

“Mrs. May’s math class looks very different than it did a few years ago,” says Droke. “Boys are learning in different ways and on a different timetable. Some are working in small groups while others are conferencing one-on-one with the teacher or learning coach or even a virtual tutor. Some are using a specialized math program on their laptop, while other boys are working on a project. Learning approaches depend on what the learner needs that day and how he best learns. There is great energy and focus in the classroom, and the boys have a greater sense of ownership of their learning.”

The customized learning approach at PDS can be described as each boy journeying on a learning quest. The goal for each boy's quest is to achieve learning mastery so that he has a secure and lasting foundation for higher concepts and math reasoning to be layered upon. The example of customized learning from 5th grade at PDS explained on the following pages offers a look at how a customized approach is better for students, offering each boy an opportunity to self-direct his learning path based on his particular learning profile.

 

MyQuest-Process-SmallThe MyQuest Math Process for 5th Grade Math. The customized learning approach at PDS can be described as each boy journeying on a learning quest. The goal for each boy's quest is to achieve learning mastery so that he has a secure and lasting foundation for higher concepts and math reasoning to be layered upon.

A 5th Grade Math Quest

In 5th grade, each math quest is divided into an eight day unit. A learning objective is introduced, and each student is expected to achieve and show mastery within the eight day period. How each boy progresses towards mastery, however, depends on his particular abilities, skills, styles, and mindset at that particular time.

Classroom Instruction

During the first three days of a new quest, Mrs. May introduces the material to be mastered in a variety of ways, including class lectures. However, Mrs. May has “flipped her classroom.” The classroom is “flipped” in that homework becomes classwork and traditional class lecture becomes homework. Mrs. May posts recorded lectures of herself explaining the learning topic. Students are able to watch these lectures at night as their homework. Students are able to view the teacher's lectures once, twice, three times or more, as he chooses. And, if a student misses class, the lectures are online, so catching up or doing make-up work is a simple process. Short, frequent (often daily) assessments keep the teacher apprised of how each student is learning.

Class time is used for student to work problems while the teacher is there to give guidance and re-teach in the moment of application. Re-allocating how the teacher's time is focused and applied allows her to actively work with students as they are learning to apply new information and skills. Her expertise is better utilized working directly with students seeing how they are learning than to use class time to introduce information.

A Choice

After three days of instruction and practice with the material, each boy can decide if he would like to take the mastery assessment for the unit. There is no pressure or obligation to take the mastery assessment. There is no penalty for not passing the mastery assessment. It's just an attempt. If a boy does not pass the mastery assessment, he has strategic information he can use in working towards mastery.

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Guided Challenge

Ev-Nichol6th-Grade student Ev Nichol on the Guided Challenge.If a boy passes the the mastery assessment with a score of 90% or higher, he can spend the next four days working independently or in a small group to explore math related topics. A boy might apply what he has learned to solve real world problems, work on a math project, or he can use the time to learn a more advanced math skill that will not be covered in the traditional 5th-grade math curriculum. This time is called guided challenge.

Mrs. May meets with each student individually to help him design his challenge time. She directs each boy to particular math activities she has either designed or selected as being excellent in developing the advanced skills for which the individual student is ready. She also develops a challenge assessment to measure each student's success in learning the material he set out to learn. This time allows each boy to develop his own interests and to initiate his own learning. “On these guided challenge days, individual boys may be learning math concepts at anywhere from a 5th-9th-grade math level. Each is working at his level according to his interests,” says Mrs. May. “In a traditional math classroom, these boys would have been bored after mastering the lessons scheduled, having to wait for the teacher to continue to teach the skills they already knew. In the traditional classroom, all students must learn the same thing at the same time regardless of their mastery level.”

Learning Circuits

Boys that do not pass the mastery assessment with 90% or higher or who choose not to take the assessment early focus for the next four days on working through a learning circuit that is designed to help them learn the concept from many different perspectives and learning strategies. The learning circuit is like circuit training that one might do at the gym. Learning coaches are available to guide and support students through the learning circuit. At the end of the learning circuit, students take the mastery assessment to complete the unit. “Our various learning circuits enable us to target instruction to the particular skills that each individual needs,” says Mrs. May, “and the circuits include several different types of instruction for each learner. This greatly enhances each boy’s ability to master the skills.”

Goal: Mastery of Math

The important thing to realize about the math quest is that the learning objectives and mastery assessments are the same for each student. What is changed is how each student progresses to the learning objective. One student might pass the mastery assessment early in one unit and make use of the learning circuit in the very next unit. The important thing is that each student masters the concept, understands it deeply, and can apply and show what he knows.

On these guided challenge days, individual boys may be learning math concepts at anywhere from a 5th-9th-grade math level. Each is working at his level according to his interests...

“One of the many challenges of this approach is keeping track of where each individual student is on his customized journey,” says Chief Information Officer Cathy Kyle. “We have explored various algorithms and used our technological assets to help us chart the progression of each boy. It is vital to be able to track this.”

“It’s remarkable what we can do when really smart and adaptable teachers harness and leverage our intellectual capital and technical assets,” Kyle continues. “Being a 1:1 laptop school, and having a team of technology coordinators, learning specialists and learning coaches, have enabled us to create our customized math program which we are calling MyQuest Math.”

Designing and implementing a curriculum that adapts to the learner calls upon the teacher to be creative and flexible, yet also disciplined in systematically gathering and analyzing data on each student. “We have more frequent, yet short, assessments than before,” says Mrs.May. “Most of the assesments,” Mrs. May continues, “are for me to use in understanding what each student needs right now and what customized path he should journey down.”

Along with a small number of other outstanding schools around the country, we believe we are on the leading edge of customizing learning to the individual student, and we are delighted with the very strong results we are seeing.

Customized learning programs developed and piloted in both 1st and 5th grades during 2011-2012 were so successful in the levels of excitement, engagement, and excellence evidenced that this year PDS is extending the approach to all other elementary grade classes. The adaptive approach in math is inspiring and informing a customized reading curriculum as well. Of course, how each grade level is using customized approaches and technology is different because each grade level keeps in mind what is developmentally appropriate for the learner's age.

“While we believe that math was the most logical place to start with customizing the curriculum, we believe the approach can work in other subjects as well,” says Burns. In addition to reading, PDS has also begun some adaptive curriculum approaches with parts of our world language program. “Customizing is about being nimble and flexible in meeting each learner where he is and giving him what he needs when he needs it.”

The math program at PDS assures that each boy is strong both with computation and conceptual thinking and reasoning. Says Burns, “We've studied a variety of math programs from around the country and world, including Singapore Math, the online approach of Khan Academy, various software programs, and other traditional programs. We've pulled what we believe are some of the best elements from a number of these and other approaches, but we've created multiple paths, modalities, and timelines that each individual boy can take. We think this is a better approach to designing learning than relying on any single textbook or any single program.” Implementing a completely different approach to teaching math has engendered a number of powerful outcomes at PDS: increased understanding and performance in math across the spectrum of learners, greater responsibility, independence and ownership for their learning by students, a growth mindset about the effort required to learn effectively, decreased test anxiety, and deep engagement and excitement about math. “Along with a small number of other outstanding schools around the country, we believe we are on the leading edge of customizing learning to the individual student,” says Burns. “And we are delighted with the very strong results we are seeing.”

“While our math scores have been good in the past, we have seen large gains in student performance since we began customizing the curriculum,” says Droke. “The standardized test scores are outstanding and the highest we've ever seen. In fact, our current 6th graders have average math scores at or above the 9th-grade level.” One other important outcome of this new customized approach delights PDS: math seems to have become many PDS boys' favorite subject.

Last modified on Tuesday, 26 July 2016

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