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Standards-based assessment and Instruction


Archive for October, 2018

A Mindset Shift in Problem Solving

Monday, October 1st, 2018

By: LaToya Garcia, Asst. Principal, & Kimberly Naidu, Third Grade Teacher, at P.S. 12, Brooklyn, NY

Exemplars Problem Solving Procedure has demonstrated that students can be very creative when they are allowed to choose their own methods for solving mathematical problems. Many educators, we believe, focus on enhancing mathematics skills to meet academic expectations, but fail to promote more critical thinking. Without the ability to inquire while thinking, students will not learn to make decisions.

At our school, Exemplars has given students the opportunity to learn from one another and provide opportunities to use multiple solution strategies for the same problem. The Problem Solving Procedure has supported students in understanding a problem, identifying a strategy to use, solve the problem, communicate findings in words, and trying to solve a problem in another way.

Exemplars has also helped to prepare our teachers for a more cognitively guided instruction. Our goal was to modify our current curriculum to help students become mathematically literate citizens. We realized that problem solving wasn’t about knowing the solution to the problem, it was about understanding that knowledge. In order to enhance learning, our teachers use a student’s prior knowledge, transfer that information to new situations and organize their students’ knowledge using model-based problems from the Exemplars Library. Teachers are able to plan activities to help students build their mathematical knowledge through problem solving and reflect on the process of mathematical problem solving. Our teachers find that students connect different meanings, interpretations and relationships to the four operations in math.

Our training with Exemplars helped to develop a more differentiated learning environment as well. We now integrate mathematics across our curriculum. For example, teachers use more math read-alouds in the classroom as a visual interpretation of mathematical problems. Teachers modify problems from the Exemplars Library by simply changing the character’s name to one students recognized from a literacy lesson. Students are also provided with manipulatives to show math situations. Manipulatives and other mathematical tools are made apart of our daily routines. Materials are made accessible in math centers and students are encouraged to self-select resources when needed. Our entire school community understands that our students need to improve in the area of communication. Students practice using math language to explain what they did while solving a problem and represent their math thinking through drawings and diagrams.

Exemplars has helped to guide and organize our students’ thought processes–a skill that can be transferred to all content areas. Throughout the school, students have begun to recognize the positive impact of a problem-solving strategy guided by specific steps. A third-grade student Michael C. commented, “Exemplars is fun. It helps you to do math and writing. While you’re doing Exemplars, you can also work on your writing.” Another third-grade student Desayee S. said, “What I like about Exemplars math is that it helps me to practice using different strategies for math, like diagrams, models and tables.”

Additionally, Exemplars has led to an increase in student-to-student conversation in students who had previously shied away from mathematics and students who are currently learning English as a second language.

As the year continues and students become even more experienced Exemplars math problem-solvers, we anticipate an improvement in students’ critical thinking and problem-solving skills. Students have already begun to develop a love for mathematics and are learning to persevere until they arrive at their answer.



10 Things Educators Love About Exemplars, Plus 1 Big Bonus

Monday, October 1st, 2018

We asked a powerhouse teaching team to share their Exemplars experience. In an inspirational conversation, a panel of educators at Brooklyn’s PS 12 offered ten amazing ways that using Exemplars has transformed their school.

1. It encourages students to be flexible and creative in their approach to solving problems. “My students love the freedom Exemplars tasks give them,” says Kimberly Naidu, a third-grade teacher. “They’re never forced to use a specific strategy. They can create one or use one they’ve learned before.”

2. It builds students’ math vocabulary. Aldine Finnikin-Charles, an experienced special education teacher, says, “My students are always using math nicknames,” says Aldine, “so the tasks that require them to use at least two math vocabulary terms really help them a lot.”

3. It helps students become capable peer and self-assessors. PS 12 teachers ask students to consider their own work alongside Exemplars anchor papers. “It really helps them get a good understanding of how to meet the standard,” says Kimberly. “They see exactly what needs to be done.”

4. It spurs students to demonstrate their understanding. They learn to communicate their ideas clearly and effectively. Plus, it’s fun, says Cherron Knight, who teaches grades 4 and 5: “Our students love showing their strategies. They can always argue, ‘Why did you use that strategy?’ They love that part, explaining what they think.”

5. It motivates students to make new mathematical connections. “When kids bring their work up to me, I say, ‘Go back and see what else you can do. What’s a different way of showing it?’ They find that enjoyable,” says Kimberly, “because they can always do it another way.”

6. It lets students practice a process for solving problems — so they can internalize it and apply it to every task. “That’s the greatest thing,” says Aldine, “the best thing for them. They are able to become reflective thinkers.”

7. It gives students a clear understanding of what kind of work meets the standards. Kimberly says, “They really want to become Experts,” and because of the Exemplars rubric, “they know exactly what needs to be done to achieve that level.”

8. It empowers students as peer and self-assessors. With what Principal Nyree Dixon calls “these amazing rubrics” that are at the heart of Problem Solving for the 21st Century, “they’re not waiting for the teacher,” she says. “They are not waiting for quote-unquote ‘authority.’ They are assessing their work themselves,” and experiencing the benefits.

9. It inspires students to grow as problem solvers — and as leaders, too. When kids solve Exemplars tasks in a problem-solving classroom, they become the experts. And they become skilled collaborators and advocates, Nyree says. “They’re learning to work together and disagree or agree,” she explains. “They’re learning to take a stance and defend their responses and answers.”

10. It helps educators establish a classroom culture of problem solving. In a lot of schools, this constitutes a major shift in thinking. “We went through growing pains. We still do,” Nyree says. “We have to keep our minds open and be willing and ready to learn.” And we’re there to help them every step of the way. After all, every teacher in every school should be able to say, as Nyree does, “We do not ever, ever, ever lower our expectations.”

The PS 12 team reported another benefit, too: Their students made a dramatic jump in math scores on standardized tests, an improvement they attribute to Exemplars — but more importantly, students made enormous strides forward as problem solvers.

“I think Exemplars did a really, really good job in helping the students to think critically about the math that they were learning,” says LaToya Garcia, Assistant Principal. “Exemplars really gave them the practice and support that they needed to be able to not only solve the problem but also to solve it using multiple strategies, critically think about how they could expand the problem, and explain their thinking in a precise way.”

Our thanks to the team at PS 12 for sharing their insights. We’re thrilled to be a part of your students’ success.

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