SecIII13_Day3

Pedagogy: Assessment

 * > ** Sec III Home ** ||||> **Day 1** ||> **Day 2** ||> **Day 3** ||> **Day 4** ||

Documents

 * [[file:DU3_Grow_It_Funny_SecIII.pdf|DU3_Grow_It_Funny_SecIII.pdf]]
 * [[file:SU3_Slice_Away_SecIII.pdf|SU3_Slice_Away_SecIII.pdf]] - double sided/separated
 * [[file:PU3_Fit_It_SecIII.pdf|PU3_Fit_It_SecIII.pdf]] - single sided/separated
 * [[file:Assessment Items.pdf|Assessment Items.pdf]]
 * [[file:StandardsofMathematicalPracticeAllononepage.pdf|StandardsofMathematicalPracticeAllononepage.pdf]]
 * [[file:Task Analysis Guide.pdf|Task Analysis Guide.pdf]]
 * [[file:Feedback_form_day3.pdf|Feedback_form_day3.pdf]]


 * Facilitation Notes**

Day 3: Instructional Practice: Assessment

As they come in, on Post-it Notes, write down what the launch, explore, and discuss means to you and post it on the three parts of the learning cycle from the day before. Clarify Teaching Cycle, using portions of powerpoint as needed. || CMI Powerpoint, Chart with teaching cycle || Math Focus: 2-dimensional cross-sections of solids, volume and density || Project image of cubical watermelon ||
 * Time || Task || Materials ||
 * 8:30 - 8:45 || CMI Framework - deepening the ideas of the **teaching** cycle “Re-view”
 * 8:45 - 9:30 || __Develop math Task: __Grow It Funny
 * //Notes: //


 * <span style="font-family: Cambria,serif;">Follow the outline of the teaching notes in <span style="color: #cc0000; font-family: Cambria,serif;">[[file:DU3_Grow_It_Funny_SecIII_TN.pdf|DU3_1_Grow_It_Funny_TN]] <span style="font-family: Cambria,serif;"> for launch, explore and discuss
 * <span style="font-family: Cambria,serif;">Journal entry should be inserted as is from the collective handout (glue in) <span style="color: #c00000; font-family: Cambria,serif;">[[file:DU3_Grow_It_Funny_SecIII_TN.pdf|DU3_Grow_It_Funny_Collective]] ||
 * <span style="font-family: Cambria,serif;">9:30 - 10:00 || <span style="font-family: Cambria,serif;">Pedagogy Focus: Content Knowledge Standard 4 ||  ||
 * //<span style="font-family: Cambria,serif;">Notes: //

<span style="font-family: Cambria,serif;">What content knowledge do you need in order to plan your instruction for the Grow It Funny task? <span style="font-family: Cambria,serif;">i. How did you determine your map? <span style="font-family: Cambria,serif;">ii. What experiences led you to that particular map? <span style="font-family: Cambria,serif;">iii. What knowledge is necessary as you plan activities such as ones we have engaged in? * Note here that the process of planning contributes to content knowledge development. <span style="font-family: Cambria,serif;">iv. What central concepts, tools of inquiry, and structures of the discipline are necessary to understand? How are representations used? <span style="font-family: Cambria,serif;">Turn to page 12-13 of UETS for detailed description - pay attention to the strands and descriptors for the practicing, effective and highly effective teachers. How do you see teachers moving from one category to the next? || <span style="font-family: Cambria,serif;">Are there misconceptions that need to be clarified, are there ambiguities that need clarifying, are there generalizations that would be helpful for them to consider, identifying where in the conceptual understanding the student resides, are there opportunities for one students’ thinking to push another student. These are just some of the areas to think about. How can we effectively use formative assessment strategies during the teaching cycle? || <span style="font-family: Cambria,serif;">Student work || <span style="font-family: Cambria,serif;">Math Focus: Discover the relationship between the volume of ellipsoid and the dimensions of its cross sections. ||  ||
 * 1) <span style="font-family: Cambria,serif;">a. Make a concept map of the content surrounding the topic of study – big ideas and connections should be clear. Add fine grain at the end. Share and compare different maps using document camera.
 * 2) <span style="font-family: Cambria,serif;">b. Questions:
 * <span style="font-family: Cambria,serif;">10:00 - 10:15 || <span style="font-family: Cambria,serif;">Pass out student work. Ask participants to review the work and consider what could be the next questions that would push the students to the next stage of development?
 * || <span style="font-family: Cambria,serif;">Break ||  ||
 * <span style="font-family: Cambria,serif;">10:15 - 11:30 || __<span style="font-family: Cambria,serif;">Solidify Task: __<span style="font-family: Cambria,serif;">Slice Away
 * //<span style="font-family: Cambria,serif;">Notes: //


 * <span style="font-family: Cambria,serif;">This task was designed for teachers to feel as if they were in the role of being a student.
 * <span style="font-family: Cambria,serif;">Follow the outline of the teaching notes in <span style="color: #cc0000; font-family: Cambria,serif;">[[file:SU3_Slice_Away_SecIII_TN.pdf|SU3_1_Slice_Away_TN]] <span style="font-family: Cambria,serif;"> for launch, explore and discuss.
 * <span style="font-family: Cambria,serif;">As part of the discussion, consider what modifications could be made to the task to allow use in the classroom.
 * <span style="font-family: Cambria,serif;">Do not forget to enter the journal entry – see the teaching notes. ||
 * <span style="font-family: Cambria,serif;">11:30 – 12:15 || <span style="font-family: Cambria,serif;">--- Lunch --- ||  ||
 * <span style="font-family: Cambria,serif;">12:15 - 1:15 || <span style="font-family: Cambria,serif;">Pedagogy Focus: Assessment *

<span style="color: windowtext; font-family: Cambria,serif;">“Assessment Discussion Questions.docx”, 1 for each small group. <span style="color: windowtext; font-family: Cambria,serif;">Chart paper for summary definition of assessment item. <span style="color: windowtext; font-family: Cambria,serif;">“Assessment Items.docx” Handout, 1 for each participant, double sided. <span style="color: windowtext; font-family: Cambria,serif;">“Task Analysis Guide.pdf” Handout, 1 for each participant. <span style="color: windowtext; font-family: Cambria,serif;">Chart paper for the Assessment Item analysis. <span style="color: windowtext; font-family: Cambria,serif;">Poster and markers for each group. <span style="color: windowtext; font-family: Cambria,serif;">Poster with Summary Questions.

__<span style="font-family: Cambria,serif;">* You can read more in __ || <span style="font-family: Cambria,serif;">See to the left || <span style="color: windowtext; font-family: Cambria,serif;">The purpose of this session is to lead participants to build their talents for creating relevant assessment items to use on unit tests, and expand ideas for formative assessment throughout the instructional unit. Participants have practiced creating rich mathematical tasks for lesson activities, but here we want to emphasize that we need to monitor, assess, and give good feedback to our students through continual assessment and pertinent summative tests.
 * **<span style="color: windowtext; font-family: Cambria,serif;">Overview and Purpose: **

<span style="color: windowtext; font-family: Cambria,serif;">Participants will examine test items developed for a 7th grade unit on circles, evaluate the examples based on cognitive level and the mathematical practices in the Utah Core, and then design a test item and rubric of their own.


 * <span style="color: windowtext; font-family: Cambria,serif;">1. Initial Discussion Questions. **<span style="color: windowtext; font-family: Cambria,serif;">Hand each table these 3 questions printed on a slip of paper.


 * <span style="color: windowtext; font-family: Cambria,serif;">What are important features of an assessment item you would use on a test? **


 * <span style="color: windowtext; font-family: Cambria,serif;">How do you continually assess your students’ progress on your intended learning objectives throughout the course of a learning cycle? **


 * <span style="color: windowtext; font-family: Cambria,serif;">Do you use different assessment strategies depending on where you are in the cycle? Explain. **

<span style="color: windowtext; font-family: Cambria,serif;">Ask participants to discuss each question in small groups (5 minutes), then call on groups to share back responses.

<span style="color: windowtext; font-family: Cambria,serif;">Bring out that an assessment item consists of a prompt and a rubric. Also bring out that an assessment item must have mathematical content relevance and level of cognition relevance. <span style="color: windowtext; font-family: Cambria,serif;">Assessment is done continually throughout the learning cycle with formal and informal questioning and gathering of data. Teachers may bring up various polling strategies they use, how they collect and provide feedback on written work, and strategies to give students the chance to self-assess and give feedback to one another. Try to bring out some strategies for helping students keep their written work organized in a notebook and some ideas for how these notebooks can be useful for formative assessment.

<span style="color: windowtext; font-family: Cambria,serif;">Here is an example of what might surface about assessment in different parts of the learning cycle:

<span style="color: windowtext; font-family: Cambria,serif;">Develop understanding – Students are engaged in constructing concepts, discovering mathematical relationships, and comprehending and explaining new mathematical connections, so using multiple representations and lots of examples (and non-examples) is helpful. For assessment and learning tasks, use high cognitive demand tasks and ask students to provide explanations. Here we would expect students to use inductive reasoning for the most part… generalizing from many specific examples.

<span style="color: windowtext; font-family: Cambria,serif;">Solidify understanding – In this stage of the learning cycle students may refine concepts and relationships they discovered in the first part of the cycle. They will likely need to learn precise definitions, and multistep procedures. Hence error pattern analysis, and careful feedback on student written work is important. They may also begin using deductive reasoning to provide mathematical proofs and explanations for theorems and relationships of the unit.

<span style="color: windowtext; font-family: Cambria,serif;">Practice understanding – Once in this stage of the learning cycle, students should be well equipped to handle complex problem solving tasks. Assessment should give students chances to apply and explain the particular mathematical content in new situations. Students will also develop fluency with memorization and procedural information.

<span style="color: windowtext; font-family: Cambria,serif;">Make a chart of a summary definition of assessment item. (Include prompt, rubric, and relevance.) If desired also chart assessment strategies. (8 minutes)


 * <span style="color: windowtext; font-family: Cambria,serif;">2. Assessment Items Examples. **<span style="color: windowtext; font-family: Cambria,serif;">Ask each group to read through the handout and use the Mathematical Practice Standards and Levels of Cognitive Demand to evaluate each item. Ask them to refer to the Practice Standards in their Utah Core, and the Task Analysis Guide Handout. (18 minutes)

<span style="color: windowtext; font-family: Cambria,serif;">What Mathematics Practice Standards do the items require of students? <span style="color: windowtext; font-family: Cambria,serif;">What Level of Cognitive Demand best describes each item? <span style="color: windowtext; font-family: Cambria,serif;">Would this be useful on a test? Why or why not? <span style="color: windowtext; font-family: Cambria,serif;">How can the Levels of Cognitive Demand and the Mathematical Practice Standards help us to create effective assessment items to yield a broad picture of our students’ mathematical performance? <span style="color: windowtext; font-family: Cambria,serif;">What mathematical practices are not assessed through these questions and how might you design an item to do so? <span style="color: windowtext; font-family: Cambria,serif;">How do these items compare to typical test questions?
 * <span style="color: windowtext; font-family: Cambria,serif;">Circulate and prompt groups with these questions: **

<span style="color: windowtext; font-family: Cambria,serif;">The table below shows my ratings, where cognitive levels are: 1 for memorization, 2 for procedures without connections, 3 for procedures with connections, and 4 for doing mathematics. If desired, chart ratings for all participants during the discussion. (10 minutes) || <span style="color: windowtext; font-family: Cambria,serif;">Item || <span style="color: windowtext; font-family: Cambria,serif;">Cognition Level || <span style="color: windowtext; font-family: Cambria,serif;">Mathematical Practices || <span style="color: windowtext; font-family: Cambria,serif;">Notes || <span style="color: windowtext; font-family: Cambria,serif;">(discovery) || <span style="color: windowtext; font-family: Cambria,serif;">1, 7 || <span style="color: windowtext; font-family: Cambria,serif;">Sends message that engaging in discovery is important. || <span style="color: windowtext; font-family: Cambria,serif;">(reasoning) || <span style="color: windowtext; font-family: Cambria,serif;">3, 4, 6 || <span style="color: windowtext; font-family: Cambria,serif;">Comprehension of the mathematical relationship and explaining the reasoning is the emphasis of this prompt. || <span style="color: windowtext; font-family: Cambria,serif;">(memorization) || <span style="color: windowtext; font-family: Cambria,serif;">6 || <span style="color: windowtext; font-family: Cambria,serif;">Typical test prompt, but also likely available for students to look up on a reference sheet somewhere. || <span style="color: windowtext; font-family: Cambria,serif;">(memorization, appreciation) || <span style="color: windowtext; font-family: Cambria,serif;">none || <span style="color: windowtext; font-family: Cambria,serif;">Hey, wait, is this in the Core? || <span style="color: windowtext; font-family: Cambria,serif;">(procedural) || <span style="color: windowtext; font-family: Cambria,serif;">2, 6 || <span style="color: windowtext; font-family: Cambria,serif;">Often called an application this really doesn’t require students to evaluate whether or not a particular formula should be used. || <span style="color: windowtext; font-family: Cambria,serif;">(problem solving) || <span style="color: windowtext; font-family: Cambria,serif;">4 || <span style="color: windowtext; font-family: Cambria,serif;">Perhaps an extended performance task. || <span style="color: windowtext; font-family: Cambria,serif;">(Is it non-mathematical activity?) || <span style="color: windowtext; font-family: Cambria,serif;">2, 3 || <span style="color: windowtext; font-family: Cambria,serif;">Creative thinking – what if we test this? What if we don’t? ||
 * <span style="color: windowtext; font-family: Cambria,serif;">Discussion. **
 * <span style="color: windowtext; font-family: Cambria,serif;">A || <span style="color: windowtext; font-family: Cambria,serif;">1 or 3 (conceptual) || <span style="color: windowtext; font-family: Cambria,serif;">2, 6 || <span style="color: windowtext; font-family: Cambria,serif;">Requires not just recall, but conceptual understanding. ||
 * <span style="color: windowtext; font-family: Cambria,serif;">B || <span style="color: windowtext; font-family: Cambria,serif;">2 or 3
 * <span style="color: windowtext; font-family: Cambria,serif;">C || <span style="color: windowtext; font-family: Cambria,serif;">3 or 4
 * <span style="color: windowtext; font-family: Cambria,serif;">D || <span style="color: windowtext; font-family: Cambria,serif;">1
 * <span style="color: windowtext; font-family: Cambria,serif;">E || <span style="color: windowtext; font-family: Cambria,serif;">1
 * <span style="color: windowtext; font-family: Cambria,serif;">F || <span style="color: windowtext; font-family: Cambria,serif;">2
 * <span style="color: windowtext; font-family: Cambria,serif;">G || <span style="color: windowtext; font-family: Cambria,serif;">4
 * <span style="color: windowtext; font-family: Cambria,serif;">H || <span style="color: windowtext; font-family: Cambria,serif;">4


 * <span style="color: windowtext; font-family: Cambria,serif;">3. Design Time. **<span style="color: windowtext; font-family: Cambria,serif;">Instruct each group to work for 10 minutes to write a prompt with a rubric that can assess student thinking (and respond to it), related to the learning cycle they just participated in. Ask them to write their result on a poster, and in their notebooks. Have a quick gallery walk to share assessment items. (2 minutes)


 * <span style="color: windowtext; font-family: Cambria,serif;">4. Summary. **<span style="color: windowtext; font-family: Cambria,serif;"> (7 minutes) Ask everyone to record a summary of this discussion in the notebooks. The summary may include answers to the following questions:


 * <span style="font-family: Cambria,serif;">What assessment questions/formats can we use to capture a lot of student thinking with a few quick questions?
 * <span style="font-family: Cambria,serif;">How can the notebook afford us opportunities for collecting written responses?
 * <span style="font-family: Cambria,serif;">How can a rubric facilitate our work providing feedback to students?
 * <span style="font-family: Cambria,serif;">1:15 - 2:45
 * <span style="font-family: Cambria,serif;">1:15 - 2:45

<span style="font-family: Cambria,serif;">Break as needed || __<span style="font-family: Cambria,serif;">Practice: __<span style="font-family: Cambria,serif;"> Fit It / Mold It <span style="font-family: Cambria,serif;">Math Focus: Efficiency, density, modeling ||  || <span style="font-family: Cambria,serif;">Think both in terms of your own context and in terms of issues that may be common to all groups.
 * //<span style="font-family: Cambria,serif;">Notes: //
 * <span style="font-family: Cambria,serif;">Follow the outline of the teaching notes in <span style="color: #cc0000; font-family: Cambria,serif;">[[file:PU3_Fit_It_SecIII_TN.pdf|PU3_Fit_It_TN]] <span style="font-family: Cambria,serif;"> for launch, explore and discuss
 * <span style="font-family: Cambria,serif;">Journal entry in this case should be individually written reflection to be completed after the project presentations.
 * <span style="font-family: Cambria,serif;">What type of assessment items could be used to assess the work done during the practice task, Fit It/Mold It? (projects, extended performance tasks) ||
 * <span style="font-family: Cambria,serif;">2:45-3:15 || <span style="font-family: Cambria,serif;">Pedagogy Focus: Assessment ||  ||
 * //<span style="font-family: Cambria,serif;">Notes: //
 * <span style="font-family: Cambria,serif;">How might assessment of a practice task at the end of a learning cycle be different than assessment during or after a solidify task? (conceptual & discovery à <span style="font-family: Cambria,serif;"> comprehension & mastery)
 * <span style="font-family: Cambria,serif;">Look at the Secondary III Core and Curriculum Guides. What standards were addressed today? Design additional assessment items pertaining to the mathematics that needs to be developed, solidified, and practiced.
 * <span style="font-family: Cambria,serif;">If we write good tests for our students, how will this help our students achieve on state and national tests?
 * <span style="font-family: Cambria,serif;">If time is available, have participants write assessments for the work that they did on the previous days. ||
 * <span style="font-family: Cambria,serif;">3:15 - 3:30 || <span style="font-family: Cambria,serif;">Distribute the feedback form || <span style="font-family: Cambria,serif;">Feedback form day 3 ||
 * || <span style="font-family: Cambria,serif;">Facilitator reflection and planning time to use feedback to inform the next day’s practices. Reflect on scheduling and on learning objectives and analysis of learner experiences.
 * ● <span style="font-family: Cambria,serif;">How did we meet today’s objectives?
 * ● <span style="font-family: Cambria,serif;">What schedule adjustments need to be made?
 * ● <span style="font-family: Cambria,serif;">How did we work together as facilitators?

<span style="font-family: Cambria,serif;">Email facilitator groups to share insights and suggestions for improving the academy in subsequent weeks. ||  ||