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Standards-based assessment and Instruction


Archive for October, 2014

A Problem-Solving Lab to Support the Math Practices

Friday, October 31st, 2014

Written By: Donna Krachenfels & Debra Sander, Teachers from PS 54

The school administrators at PS 54 had a vision to create a math laboratory based on the eight Standards of Mathematical Practice. The idea was to create a setting in which students could focus on multi-step problem solving.

The Exemplars program has given our students many opportunities to build and strengthen their problem-solving skills. Students were also able to strengthen their close reading skills as they reread problems multiple times to identify and think about the relevant information necessary to find a solution. Collaboration allowed students to become confident in their problem-solving skills and increased their abilities to construct viable arguments as they defended their solutions and critiqued the solutions of their classmates. Students were not afraid to take risks as they tried different representations and strategies to solve problems. As a result of the Exemplars math program, our students became more confident and more independent problem solvers.

The math laboratory is in its second year at PS 54. Last year, our data saw increased math scores for the classes that participated in the problem-solving lab. This year, the trend continued and all general education students passed the state math exam.

Special thanks goes to Exemplars professional development consultant Deb Armitage for all of her help and support. She is a true math educator!

The Future Depends on Problem Solving

Tuesday, October 7th, 2014

By: Ross Brewer, Ph.D., Exemplars President

Students working collaboratively on an Exemplars math task.

Once upon a time, Americans might have been content to live in a community much like Garrison Keillor’s Lake Wobegon, “where all the children are above average.” That’s because historically American kids, and our schools, were above average; however, for decades, America’s education system has been losing ground internationally. In an era when knowledge-based competition comes from every corner of the globe, average is no longer good enough for American students or workers. American jobs are becoming increasingly vulnerable as technology becomes more sophisticated and overseas workers better educated. Both of these are happening at an accelerated rate.

Because of the disruptive changes occurring in our knowledge-based economy, the good jobs—jobs that pay high wages—that will survive are those that require higher cognitive skills.

For years, economists and educational experts have been warning about the impact that the increasingly rapid development of technology is likely to have on unskilled workers. MIT professors Brynjolfsson and McAfee offer this stark summation of current technological trends:

Technological progress is going to leave behind some people, perhaps even a lot of people, as it races ahead. … there’s never been a better time to be a worker with special skills or the right education, because these people can use technology to create and capture value. However, there’s never been a worse time to be a worker with only ‘ordinary’ skills and abilities to offer, because computers, robots and other digital technologies are acquiring these skills and abilities at an extraordinary rate. (The Second Machine Age, p11)

Unfortunately, as the most recent international reports make clear, while American students have made incremental improvements on international tests of problem solving, the position of the United States continues to slip as other nations advance more rapidly.

One of the reasons for weak student performance on international tests has historically been the absence of consistently strong standards from state to state. In the past, many standards have lacked focus and coherence, giving prominence to simple skills that are easily measured while minimizing problem solving and communication, skills employers identify as being important.

Why is problem solving so important? At a mathematical level, problem-solving skills are critical to the development of understanding more advanced mathematics and the ability to perform other complex tasks. This in turn creates the foundation to solve problems in the real world. Indeed, among the essential employee skills identified by employers are the ability to solve problems, process information, analyze quantitative data and to communicate verbally and in writing.

Thankfully, we are in the midst of a transformation whose aim is to close the global competitiveness gap and prepare our children for a global economy.

Through the adoption of the new math TEKS in 2012, Texas has moved to address weaknesses in problem solving and the associated process skills. In addition to content standards, the new TEKS include a strong emphasis on mathematical process standards.

(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) apply mathematics to problems arising in everyday life, society, and the workplace;

(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

(E) create and use representations to organize, record, and communicate mathematical ideas;

(F) analyze mathematical relationships to connect and communicate mathematical ideas; and

(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

At least 75% of the test questions on the STAAR, the assessment designed to evaluate performance in achieving the TEKS, will incorporate math content and process standards, including problem solving.

How Exemplars Supports Problem Solving

So how does Exemplars tackle the problem-solving imperative facing today’s teachers and students in Texas? We were founded more than 20 years ago with a single mission: to engage students’ interests and develop their abilities to problem-solve in today’s world. From the beginning, the focus of our mathematics material has been on the following process standards: problem solving, reasoning, communication, representation and connections. Exemplars tasks are designed to help teachers instruct students in mathematical problem solving and to allow students to demonstrate their understanding of problem solving.

Our latest K–5 material, Problem Solving for TEKS, offers teachers supplemental performance tasks to develop their students’ problem-solving and critical-thinking skills. By organizing the new TEKS into rich Units of Study, this resource is designed to assist Texas educators in teaching a focused mathematics curriculum. Our real-world tasks, rubrics and anchor papers are designed to encourage:

  • Students’ problem-solving abilities
  • Students’ use of representations and making the link between the problem and the underlying mathematics
  • Students’ ability to communicate mathematical thinking and provide reasoning and proof to justify their answer or approach
  • Students’ application of appropriate mathematical language and notation
  • Students’ self-assessment skills
  • Formative assessments, which allow teachers to understand how their students are doing and to adjust their instruction to improve performance
  • Engaging summative assessments, which allow teachers to evaluate if their students have met the standard

In short, problem solving is at the core of everything we create at Exemplars. You can try our new material with your students by signing up for a free 30-day trial or by downloading sample tasks. Let us know what you think.

Exemplars | 271 Poker Hill Road | Underhill, Vermont 05489 | ph: 800-450-4050 | fax: 802-899-4825 |

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