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In Principles to Actions, the National Council of Teachers of Mathematics (NCTM) calls for the implementation of tasks that “promote reasoning and problem solving” (p. 10) as one of eight “research informed teaching practices” (2014, p. 7). We argue that the implementation of high-level tasks affords opportunities for teachers to then engage in the other research informed teaching practices recommended in Principles to Actions. These teaching practices include using and connecting mathematical representations, facilitating meaningful mathematical discourse, posing purposeful questions, building procedural fluency from conceptual understanding, supporting productive struggle, and eliciting and using evidence of student thinking (NCTM, 2014). For instance, students cannot be prompted to make connections between mathematical representations if the task does not afford the opportunity to do so. Further, teachers and students cannot make connections between mathematical representations if they all create the same representation. 

Project TASK supports approximately 80 elementary teachers in their identification, implementation, and reflection of high-level tasks. In grade-level groups (K-5), six instructional leaders comprising faculty from Drake University, math consultants from Heartland AEA, and teacher leaders in Des Moines Public Schools are providing sustained professional development around the implementation of high-level tasks. 

Rich Mathematical Tasks

To get started, we provided teachers with three print resources: Teaching Student-Centered Mathematics (Van De Walle, Lovin, Karp, & Bay-Williams, 2014), Problem Solving for All Seasons (Markworth, McCool, & Koziak, 2015) and Mine the Gap (SanGiovanni, 2016). We used Teaching Student-Centered Mathematics to provide teachers with rationale and a foundation for teaching through problem solving. Problem Solving for All Seasons offers rich tasks organized around cultural activities that occur during the four seasons. Iowa Core standards and Standards for Mathematical Practice are identified for each task. Mine the Gap includes hundreds of tasks that promote thinking and reasoning aligned to the Iowa Core State standards. In Mine the Gap, there are subsequent tasks that follow up or add to the primary tasks, which promote continued mathematical opportunities for students. After teachers pose tasks, we ask them to reflect on task implementation and student work. 

We chose one task per month for all teachers to pose to their students. For example, we asked the fourth and fifth grade teachers to pose Task 17A from Mine the Gap, Grades 3-5 (see below). 

Mathematics figures that represent 1/4

We found Task 17A to be particularly productive for our students because their experiences, background knowledge, and perspectives on fractions differed immensely. Because of this, the conversation and deliberation between the students was tremendous! 

Through our project work, we are learning more about how students respond to tasks and how we can adapt tasks to make them more productive for students. We asked our third grade teachers to pose The July Fireworks Task from Problem Solving for all Seasons (Markworth, McCool, & Kosiak, 2016) below: 

The city of San Francisco is planning a very special fireworks show for the Fourth of July. In addition to their standard fireworks, the organizers are including special fireworks that will go off at specific times, as shown in the table:

Firework Timing
White Chrysanthemum Every 2 minutes
Blue Bloom Every 3 minutes
Red Explosion Every 5 minutes

If the organizers want to start and end the fireworks show with all three of these special fireworks going off together, how long could the fireworks show be? Explain your reasoning.

Teachers found that the task was inaccessible to many students. Thus, we generated a list of adaptations that could be used to make the July Fireworks Task more accessible:

  • Change the task to include just two fireworks
  • Change the number choices to 2, 3, and 4
  • Change the order of the fireworks to have Red Explosion first. When students were listing multiples, they did not go very far in their counting. If Red Explosion is first, students might go farther in their listing of multiples.

An adapted Fireworks Task could be given before the original to provide students with an entry point. 

Teacher Julie Zimmer wrote the following reflection about the benefits she sees from her involvement with Project Task:

I feel very fortunate to be a part of Project Task and have enjoyed seeing my students develop confidence as mathematicians. I have a culturally diverse class with varying mathematical background, who have grown from the weekly exposure to rich tasks related to the Iowa Core standards. It is amazing to see their self-esteem increase regarding their ability to work through meaningful problems when given an opportunity to make connections to the problem and converse with others. One of the most important things I have learned is to incorporate visuals at the beginning of every problem. This allows all students the ability to formulate thoughts and ideas related to the mathematical task in a non-threatening way. In addition, it incorporates the arts, which is a building goal as a Turnaround Arts school.

Once they have engaged their mind through visuals and conversations, students get to work on their own to grapple with the given tasks. They are more willing to try their best after making these connections to the problem. Then the real magic begins – when they share their thinking with others. They construct and defend their positions in a way that never would have come to life without these tasks. I have seen my students get excited about tasks and able to persevere through problems that they may have initially said were too difficult. Most recently, it came to life when defending why one part shaded out of four cannot be one fourth if the pieces are not equal. The opposing view was sure that it was one fourth because there was one shaded out of four, bringing to play the importance of size of fraction pieces.

Problem solving in mathematics supports real-world thinking and problem solving. The greatest challenge seems to be, “Where do I start?”  What we have learned and observed over the course of this professional development is that you simply start. Provide students with a rich mathematical task, that’s it! Watch, listen, and observe as students find and use strategies that make sense to them, reason through errors, collaborate with peers, and much more. Where will you start? What rich mathematical tasks make sense for you and your students?

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Posted by : jennifer.krieger

exclamation point in the middle of question markWhat do you remember about your K-12 social studies experience? Did you experience a classroom centered around exploring compelling questions? Did you analyze a variety of text, both primary and secondary sources? Primary sources are original sources from the time period and secondary sources are interpretations of those original sources. Did you have the opportunity to develop disciplinary arguments based off those texts? In other words, did you get the opportunity to think like a historian or geographer? Did you have the opportunity to identify issues in your community, state, nation, or world and think about how to address those issues? These are best practices in social studies that Iowa’s new social studies standards emphasize in order to prepare students for college, career, and civic life.

New standards often call for discussion and reflection on the instructional changes that will be necessary to best implement those standards. Iowa’s social studies standards focus on four instructional shifts that are needed in order to implement the standards with fidelity. They are as follows:

Craft questions that spark and sustain an inquiry.

Social studies is really about questions, not answers. Of course, answers are important, but it is the ability to wrestle with compelling and supporting questions and develop arguments around those questions that define good disciplinary practice in a social studies classroom. This shift asks teachers to purposefully develop compelling and supporting questions that can sustain inquiry throughout a unit of instruction.

Compelling questions are those that focus on the “big idea” of a unit of instruction. These questions are intellectually challenging, generally have no one “right” answer and compel students to argue with evidence in order to answer the question. Generally, there is one compelling question used throughout a unit. Supporting questions scaffold students’ investigations into the ideas and issues behind a compelling question. In other words, they are a way to unpack the compelling question. Generally, these questions get into the content knowledge students would need in order to effectively make an argument about the compelling question. An example:

Compelling Question: What would compel people to move to a new place?

Supporting Questions:

  • Why do people move or choose to immigrate?
  • What did immigrants experience when they arrived in America?
  • How does one’s culture influence where they choose to live?

Integrate content and skills purposefully.

Content is vitally important in a social studies classroom. But the application of the disciplinary skills of social studies is equally important. The shift asks for a balance between content and skills. In the above example about compelling and supporting questions, for example, you can see that the questions require students to access a lot of content in order to make an effective argument. However, students will need to have several social studies skills in order to be able to make an effective argument such as being able to analyze primary and secondary sources, the ability to deeply evaluate the claims a source is making, critique the reliability of sources, corroborate several pieces of evidence in order to make an effective argument, and write to name a few.

This shift also demands the use of multiple primary and secondary sources in the classroom. If students will develop an argument about the above questions, they must have access to multiple sources to help them make that argument. These sources should be tightly aligned to the compelling and supporting questions so that the inquiry can be sustained throughout the unit. 

Several examples of text sets that include compelling and supporting questions as well as primary and secondary sources aligned to those questions are available from the Iowa Department of Cultural Affairs website. The text sets were developed by the Iowa Department of Cultural Affairs and the Iowa Department of Education through a grant from the Teaching with Primary Sources program at the Library of Congress. More sets will be released in August 2018.

Provide opportunities for communicating conclusions and taking informed action.

To complete the inquiry process, teachers must now think about how they will purposefully plan for students to communicate their conclusions, and potentially take action as a result of the outcome of their inquiry. There is an expectation that social studies students practice citizenship in the same way they practice historical thinking, economic decision-making or geographic reasoning. As a result, students will need tangible opportunities both inside and outside of the classroom to consider, debate, plan for, and undertake action-oriented experiences that would culminate their academic inquiries.

Engage in rigorous, student-centered learning.

Civic readiness is a key component of the Iowa social studies standards. The idea of collaboration and student-centered learning is hard-wired into inquiry, but collaboration means more than just pairing up with other students to analyze questions or analyze sources. Rigorous student-centered learning is key for preparing students for participation in civic life.

The Iowa Department of Education has released a three-year implementation plan, with full implementation required in 2020. Implementation of Iowa’s new social studies is a process that will take time. Implementing new standards is not a task that should be done quickly or without deep thought. This year, our statewide professional development has focused on learning about these instructional shifts and the stages of planning for inquiry. In comparing this to the process of building a house, we are working on building the foundation first. Next year, we will work on building the frame of the house and get into the process of unpacking the standards. In the third year of the implementation plan, the Department will work on finalizing the exterior and interior of the house by focusing on what good assessment of the standards looks like. Each year, the Department will offer professional development and resources based on the stage of implementation we are in.

Iowa Social Studies Standards

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Posted by : stefanie.wager