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Standards-based assessment and Instruction

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Archive for April, 2019

Performance Tasks: What’s the Point?

Tuesday, April 23rd, 2019

Written by: Jay Meadows, Exemplars Chief Education Officer & Cornelis de Groot, Ph.D., Exemplars Secondary Math Editor

Twenty-five years ago, Dr. Ross Brewer, founder of Exemplars, sat in a warm farmhouse in upstate New York with Grant Wiggins and Jay McTighe and asked a very important question, “How do we determine if students can utilize the mathematics they are learning in the classroom to address and solve the complex problems they eventually will be asked to address in the “real world?” To answer this question, these leaders of education decided to employ performance tasks with the explicit purpose of putting students in the authentic role of the problem solver.

Authentic Tasks and the Skills It Takes to Solve Them

Utilizing mathematics to solve real-world or authentic tasks requires more than the foundational skills of arithmetic and calculation. Authentic tasks require the knowledgeable utilization of a combination of several mathematical concepts. To solve these tasks, a person or team must decide on a strategy, choosing which math skills and tools to utilize and in what order. Once the team has determined their strategy and arrived at a solution, they must then design a clear explanation of their solution path, demonstrate and explain their thinking and articulate the reasonableness of their solution. In essence, students must learn to develop a persuasive argument and use precise mathematical language to provide clear mathematical evidence that supports their thinking.

These problem-solving skills are not innate to most students.

The Role of Intentional Practice

To help students prepare for the journey of becoming great problem solvers, teachers must clearly explain the purpose of solving these complex tasks so students can understand why they are being asked to work on tasks that can be more challenging then they are used to.

Solving complex problems requires intentional practice. Success with performance tasks can take time. Specific stages of student understanding can be scaffolded to work methodically towards strong products. Persistent success is not going to be found if we only give performance tasks in isolation. The trajectory to mastery of problem solving can provide a rich supplement to any curriculum. Spending time having students working in teams to develop potential solution paths and develop persuasive arguments can help develop several skills which are fundamentals of the 21st Century: Collaboration, Communication, Critical Thinking, Creativity and Problem Solving.

Why Are Performance Tasks Important?

Why do we ask students to attempt performance tasks? Creating opportunities for students to practice authentic problem-solving skills within their classrooms, in safe and supportive environments, will provide them incredible opportunities to learn to create real solutions to real problems. In this way they can develop the ability to solve the problems of the 21st Century.

Performance tasks ask students to do far more than calculations. Rich performance tasks ask students to adapt and apply their developing knowledge and understanding of mathematics, to take risks and explore possible strategies, to persevere while being flexible with their mathematical skills and understandings in their efforts to become deep mathematical thinkers.

The Importance of Marinating

In this type of learning environment, the initial instructional priority is helping students to clearly understand the task they are working to solve. This goes beyond simply highlighting keywords. Instead, we must ask students to talk with each other about the task: What are they being asked to solve, what strategies have they learned in the past that may connect to this task and help them to find a solution? What do they know and wonder from the task? This time spent marinating in the task is a foundational skill for the great problem solvers throughout history. Often the most important time spent in solving a task is the time spent carefully looking at and contemplating a task. Additional time realizing how a new task connects with something the students have done in the past can provide a strategy for getting started. “How does my prior knowledge possibly connect with this new task?”

Great problem solvers spend more time marinating in a task then in any other phase of the problem-solving process.

As students work this spring to succeed on end-of-the-year performance tasks, remember these are powerful tools for preparing them to be ready to use the math concepts and skills we spend years helping them develop. These high-level expectations will help develop a generation of great problem solvers.

Exemplars Problem Solving in Our Schools

Monday, April 22nd, 2019

Written by: Phil Sanders, Elementary Math Supervisor, Plainville Community Schools, CT

For the last three years, Plainville Community School teachers have dedicated themselves to the use of the Exemplars Problem-Solving Program. There are many reasons for this. First, it is an excellent, Common Core standard aligned, comprehensive problem-solving program. Teachers from Kindergarten to grade 5 comment most often about how it really works for their students. Principals also agree that they have seen tremendous growth in students’ ability to understand a problem, develop a plan to solve a problem and create models to show their thinking about how they solved the problem.

The Challenge

Plainville has adopted a rather unique approach to tackling the issue of students being successful on pencil-and-paper math work but falling down on problem solving. Three years ago we realized that our students were not understanding what the problem-solving tasks were asking them to do, and students often failed to develop a well-thought-out plan to solve the tasks. When examining student work, teachers saw students picking numbers out of the problem and running them through the latest algorithm. When asked to discuss their thinking, students responded with confusion or lack of understanding.

A Three-Fold Solution

Exemplars has provided us with the vehicle to tackle these seemingly insurmountable issues. The program provides standard-aligned problems that lend themselves to students being successful. Our approach was three-fold: Understanding was our focus the first year, Communication the second year and Accuracy the third year.

  1. Teachers, through their district-wide PLCs, developed slideshows based on the problems, helping to create contextual understanding of what the problem was discussing. This helped activate the UDL aspect of instruction, allowing all students to gain a foothold for their understanding.
  2. Through small group work and modeling of different problem-solving strategies, students next developed their proficiency at drawing models to communicate their thinking. All this information came directly from the Exemplars Preliminary Planning Sheets, which teachers found to be crucial to understanding all aspects of the problem.
  3. Last, we focused on accuracy and found that students were ahead of the curve. Because of their developed understanding and ability to use models, students’ overall accuracy increased tremendously.

One of the ancillary benefits to the Exemplars program is that we found students were able to have either small group (Turn and Talk) or whole group discussions about what they have learned and were able to defend their findings using evidence stemming from the Exemplars problem they had completed.

Teachers find the copious amount of information included in the Exemplars program to be extremely helpful. We have incorporated Exemplars Summative problems as end-of-topic assessments, and in grades 3–5 we have seen growth of our SBAC scores. We attribute these gains to our work with the Exemplars Problem-Solving Program.

Productive Discourse and Student Choice with Exemplars

Monday, April 22nd, 2019

Written by: Brendan Scribner, 4th Grade Teacher at the Bernice A. Ray School

For the past 21 years, I’ve enjoyed the benefits of using Exemplars math problems within my classroom. The Exemplars problems are aligned to my curriculum, promote productive discourse and enable student choice. The efficient and user-friendly website allows me to spend less time planning, and more time focusing on student sense-making, intentional sharing of student thinking, and allowing for students to debate their ideas.

Laying a Foundation for Discourse

Within my 4th grade classroom, we have established ground rules for productive student discourse. It’s important to note that this foundation is built beginning on day one of the year and slowly cultivated every day. These norms help to provide a base in which we function as a learning classroom. Students must agree with and embody the norms. Students must learn and use the talk moves. We strive to have a classroom that from an outsider perspective looks, how may I say this politely, chaotic. I strive to have my students engaged in discourse related to academic talk for a minimum of 50% of all class work. It’s important that students have ownership of the talk, and I benefit greatly as the teacher listening to the discourse and planning my moves based upon the talk in the room. With a talk structure in place, this is where the Exemplars problems shine.

Classroom Norms


Student Owned Talk Moves

The Exemplars Routine

In order to support a talk rich classroom, I need to feed the learning. The Exemplars problems are rich and engaging tasks that my students eagerly unpack. With each new unit of study, I follow an instructional routine that allows students to acquire knowledge and skills in a predictable manner.

Prior to a unit of study, I visit the Exemplars Library website and review all tasks within the standard my class will be practicing. I use the summative task as my pre/post assessment for each unit. The website features underlying mathematical concepts, possible problem-solving strategies, mathematical language and symbolic notation, a planning sheet, possible solutions, and connections. These resources are user-friendly, and help to efficiently allow you as the teacher to begin to anticipate student work that will be produced for the problems presented. It is imperative that you as the teacher solve the problem on your own, and if possible, with your teaching team as well. Unpacking the problem on your own, and with colleagues, will better prepare you for guiding discourse in your classroom.

After reviewing tasks, and administering the summative as a pre-assessment, I collate all the “more challenging versions” into one condensed handout. For a recent unit: Arrays, Factors, and Multiplicative Comparison, we focused on standards 4.OA.B.4, 4.OA.A.2. As such, we used Dog Years, Feeding Lizards and Frogs, A Jumping Good Time, Making Cakes, Boxes for Mini Muffins, The Fitness Center, Hot Dogs and Buns for Friends, Marching Ants, Posters, Puppet Shows, and Snacks on the Playground. I gathered all the problems listed for these standards within one student handout. Students have a choice of which problems they attempt to solve. Students must solve at least four, then select one of the four to present to the class. To prepare the students I engage them in unpacking the grade level version of Dog Years, using a gradual release of the problem to promote contextual understanding, student engagement, and discourse.

Here is an example of how this release occurs:

Task: Dog Years

It is said that dogs age seven years for every “people year.” Mason’s dog, Shep, was born on Mason’s eighth birthday. When Mason was nine years old, Shep was seven dog years old. If Shep is fifty-six dog years old, how old is Mason? Show all your mathematical thinking.

  •  Slide1: It is said that dogs age seven years for every “people year.”
    • What do you notice?
    • Tell me 3 things about dog or people years.
  •  Slide 2:  Mason’s dog, Shep, was born on Mason’s eighth birthday.
    • Now what do you notice?
    • Are the ages of Shep and Mason a lot or a little different?
  • Slide 3: When Mason was nine years old, Shep was seven dog years old. In dog years, how old will Shep be on Mason’s twelfth birthday?
    • What do you wonder?
    • What’s the solution?
    • Estimate, how many more/less?

Scribed class anchor chart

Using a gradual release supported by classroom norms and talk moves allows for a rich and vibrant launch into problem solving. Students apply their understandings and have time to listen to all class discourse.

As the facilitator of this conversation, I scribe a class anchor chart solution for the problem. This typically includes all of the possible solutions offered on the Exemplars site. This anchor is critical as it models how we want each student to show their thinking within their math journals for every problem opportunity.

As our discussion reaches a class consensus on a solution, I then have students begin working on the Exemplars problems for the unit of study. Students will work on problems in math class each day for a part of each class session. The first two class sessions are independent work time. During the remaining class sessions, students partner with peers to engage in shared thinking time. This includes a review of work they have done alone, as well as some time working on the same problem. Again, talk moves are leveraged during partner work. After 5–7 class periods, we will begin the process of sharing our thinking.

Strategy Share Planner

In order to engage our classroom in a thoughtful and comprehensive review of the Exemplars problems, I use a strategy share planner. Students have worked toward completing at least four (many students complete all) of the problems, and now select one to share with the class. The share time often comes outside of math class. We have used snack and lunchtime effectively to ensure that we come to closure on our problems and hear from all students equitably.

Planner

We methodically review all problems solved by the class sequentially through the handout. If more than one student chose a problem, we take turns sharing each solution. This usually means we have sustained, in-depth discussions about most of the problems within the standard. This engaged sense-making opportunity allows all to share thinking, and ultimately affords us rich debates about problem-solving strategies used by all students.

Students Create Their Own Problems

A particular draw for students is the creation of their own original problem. As a result of our process of discourse, gradual release of the anchor problem, student choice, and sharing, students are typically very ready to craft their own story problems. Students write their problem and then solve them. I encourage them to use the Exemplars problem as a template. My students love to transfer their understanding and apply their developing ideas to a context that is part of their everyday life.

Using the Exemplars platform of problems has enriched my teaching practice. The resource-rich website offers readily available story problems that engage students in the practice of making sense of the world around them and appreciate that math really is everywhere. I have noticed that the intentional gradual release of problems, shared ownership of talk moves, embedded classrooms norms, and use of a strategic planner have enhanced my students’ enjoyment and success with problem-solving. I look forward to continuing to make sense of Exemplars problems with my students for many more years.

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