Focus on Formative Assessment: What makes a good response to a constructed response item? Mary Diez Rosann Hollinger Henry Kranendonk Math Teacher Leader Meeting Milwaukee Mathematics Partnership February 2006

“... Rigor has less to do with how demanding the material the teacher covers is than with what competencies students have mastered as a result of a lesson.” Tony Wagner, Rigor on Trial, Education Week, January 11, 2006

The Wagner quote signals the shift that’s required to impact student achievement – Away from a focus on disseminating information – Toward a focus on developing the learner’s ability to use critical thinking and problem solving to work with information

“Why has this been kept from us?” The cartoon about the coach and the basketball team underlines the importance of being clear about the “object of the game.” We need to make learning more accessible by making clear not only the learning targets, but also the criteria for a good performance.

“I see no need to actually physical- ly play the game ever again.” Again the cartoon about learning tennis via videotape stresses the importance of learners applying what they are learning in real world contexts. In math, it may mean the difference between memorizing an answer to a question and knowing how to address a new question because you understand the kind of question that it is.

“You’re skilled at just one thing-- taking tests” While the WKCE and other tests are important under No Child Left Behind, we can never lose sight of what we want for our children—that they have the skills and knowledge that the tests stand for.

“I expect you to be independent, innovative, critical thinkers who will do exactly as I say” We need to examine our classrooms to be sure we’re not giving mixed messages. If we want students to improve in problem solving and critical thinking, then they must be doing the work and taking the risks. We can’t do it for them. Again this underlines the difference between focusing on the right answer and focusing on the learner’s thinking process.

Feedback: “Don’t we even get a few practice semesters?” If we use assessment formatively, then we need to put aside the notion that we need to grade everything. Think about Patti Ball’

Root meaning of “assessment” Etymologically, “assessment” comes from the Latin, through the French, and means “to sit down beside” This implies a coaching relationship between teacher and student

Research on Effects (from Stiggins) Study Bloom (1984) Black & Wiliam (1996) Meisels et al. (2003) Rodriguez (2004) *Rivals one-on-one tutorial instruction S.D. Gains 1.0 to 2.0*.5 to 1.0**.7 to to 1.8** **Largest gains for low achievers

A 1.0 Standard Deviation Score Gail Equals (Stiggins): 35 Percentile Points 2-4 Grade Equivalents 100 SAT Points 5 ACT Composite Score Points U.S. TIMSS scores would move from middle of the pack to top 5

The power of formative assessment (Stiggins) Keys to Achievement Gains – Clear and appropriate targets – Accurate classroom assessment – Descriptive feedback – Student-involved assessment, record- keeping, and communication

Goals  Work with developing students’ ability to respond effectively to constructed response items as a way to focus on a need revealed in the WKCE-CRT and other data: Students show weakness in “problem solving and reasoning” and in “communication” in their performance in mathematics  Use our experience with writing short answers to specific questions that require thinking in order to “unpack” what it takes to write a good one

 Generate a set of criteria that can be used to give students feedback on their practices with writing short answers to specific questions that require thinking  Develop a plan for having students make progress in writing short answers to specific questions that require thinking for two purposes: 1) to help teachers determine next steps in teaching and 2) to help students take more responsibility for their progress

What do data tell us? Students are generally weak in – Problem Solving and Reasoning, which calls for them to question, investigate, and explore solutions to problems; think logically; justify answers to problems; and apply mathematics to everyday situations. – Communication, which calls for them to use mathematical language to express thinking, verbally and in writing; use words, metaphors and pictures to describe and explain mathematical ideas

Newmann, Bryk & Nagaoka (2001)... when “teachers organize instruction around assignments that demand higher order thinking, in-depth understanding, elaborated communication and that make a connection to students’ lives beyond school, students produce more intellectually complex work.”

Task #1 Find a partner and assign roles—”thinker” and “reporter” Solve problem Generate list of approaches to thinking that helped solve the problem

What day follows the day before yesterday, if two days from now will be Sunday?

Sample problem solving strategies Read the problem Read it again Map the information Sort the information Draw a picture or diagram or use a calendar Start with the “if clause” Start by simplifying the first clause Use “trial and error”

Task #2 Work the problem individually In pairs, look at each other’s answers and figure out what worked and what didn’t. Look diagnostically—what are the things that should go on a list of what students need to learn to do in order to answer a specific mathematics question that requires thinking? Help build a beginning formative rubric

Generating Criteria With your partner, develop the KEY FEATURES for this task on an Everyday Rubric form that demonstrates the levels of understanding Also think about writing criteria for communicating that understanding

Sample writing criteria (in kid-friendly question format) Did you  Show all your thinking?  Answer the question?  Give a clear explanation?  Write an answer that makes sense?  Write an answer that is accurate?  Give accurate and complete supporting details to explain your answer?  Write in complete sentences?  Put your sentences in an order that makes sense?

Now look at samples of student work on the same problem (yellow folder). In pairs, focus on how you might give feedback to these students. How might you guide them to improvement? To evaluate where on the rubric their understanding lies, determine what specific feedback you would give each student.

Using the Feedback Form (red folder), frame your feedback in language that indicates to students what they should re-do/revise and relearn.

Develop a plan for gathering data on how students make progress in writing short answers to specific questions that require thinking for two purposes: 1) to help teachers determine next steps in teaching and 2) to help students take more responsibility for their progress