Performance Assessments To Inform Instruction And Measure Higher Level Thinking The Mathematics Assessment Resource Service (MARS) is an NSF funded collaboration between U.C. Berkeley and the Shell Centre in Nottingham England. The Assessments target grades 2- Geometry and are aligned with the State and NCTM National Math Standards. Ramp Access Top Core Entry level (access into task) Core Mathematics - (meeting standards) Top of Ramp (conceptually deeper, beyond) Task Design
Student tests are hand scored by classroom teachers trained and calibrated using standard protocols. Students in grades 2 through 10 th /11 th grade are administered performance exams (5 apprentice tasks per exam). District scoring leaders are trained in using task specific rubrics Student results are collected, analyzed, and reported by an independent data contractor. Random sample of student papers are audited and rescored by SJSU math & CS students. (Two reader correlation >0.95) Performance Exams 40,000 – 70,000 students per year since 1999
MAC vs. CST 2012 Silicon Valley Mathematics Initiative Mathematics Assessment Collaborative Performance Assessment Exam 2012
MAC vs CST 2012 2nd GradeMAC Level 1MAC Level 2MAC Level 3MAC Level 4 Far Below Basic 1.0%0.3%0.1%0.0% Below Basic 1.9%2.4%1.2%0.0% Basic 1.3%4.8%5.5%0.3% Proficient 0.4%3.5%17.7%3.4% Advanced 0.3%0.9%23.4%31.4% 2nd GradeMAC BelowMAC At/AboveTotal CST Below 11.7%7.1%18.8% CST At/Above 5.1%75.9%81.0% Total 16.8%83.0%100%
Middle School 6th GradeMAC BelowMAC At/AboveTotal CST Below 37.2%1.4%38.6% CST At/Above 25.1%36.5%61.6% Total 62.3%37.9%100% 7th GradeMAC BelowMAC At/AboveTotal CST Below 33.3%2.1%35.4% CST At/Above 27.4%37.1%64.5% Total 60.7%39.2%100% Course 1MAC BelowMAC At/AboveTotal CST Below 34.5%3.6%38.1% CST At/Above 30.3%31.5%61.8% Total 64.8%35.1%100%
8 th Graders Taking HS Geometry Course 2 MAC Below MAC At/AboveTotal CST Below 3.1%0.8%3.9% CST At/Above 51.3%44.8%96.1% Total 54.4%45.6%100%
Use of Formative Assessment Research suggested that attention to the use of assessment to inform instruction particularly at the classroom level in many cases effectively doubled the speed of student learning.
Five elements of using assessment to inform learning The provision of effective feedback to students The active involvement of students in their own learning The adjustment of teaching to into account the results of assessment
Five elements of using assessment to inform learning The recognition of the profound influence assessment has on the motivation and self- esteem of students, both of which are crucial influences on learning The need for students to be able to assess themselves and understand how to improve
The teachers job is not to transmit knowledge. It is to engineer effective learning environments for students. The features of effective environments are that they create student engagement and Allow teachers, learners, and their peers to ensure that learning is Proceeding in the intended directions.
An important technique for helping students understanding learning intentions and success criteria is asking them to look at samples of other students work and to engage in a discussion about the strengths and weaknesses of each. Students are much better at spotting errors and weaknesses in the work of others than they are in their own.
Putting Principals into Practice Mathematical Practices Attend to precision. -use clear definitions Construct viable arguments and critique the reasoning of others. Briefly: Think of a definition for perimeter. Share with a neighbor.
Marco thinks Plan C has a larger perimeter than Plans A and B. Explain why Marco is wrong.
Look at sample work and engage in discussion about strengths and weaknesses Marco probably counted. But he counted wrong. How could this explanation be improved? What is missing to make it convincing?
Getting students engaged Plan A and B have bigger areas, so they have bigger perimeters. Do you agree or disagree? Is this sometimes true, always true, or never true?
Understanding Learning Trajectory and a Variety of Strategies Jade sold only Peanut Butter Cookie Dough. She raised $32. How many Tubs did she sell?
What do you think the student is doing? What do the lines represent? What do the numbers represent? Does it make sense?
This helps lay the foundation for proportional reasoning at later grades, for understanding input/output tables, for making graphs.
Understanding Learning Trajectory Situating the mathematics of the task in the learning trajectory for number and data: At earlier grade levels students have been learning about data collection and representation in the form of bar graphs. At this grade level students are extending the ways of displaying data to include line plots. In second and third grade students have been successfully thinking about most and least and using comparison subtraction to find the how many more. Also at third grade students have started to expand their ideas about number to include fractions, as parts of a whole, and use rulers to measure with fractions.
Understanding Learning Trajectory At this grade level students are starting to decompose a fraction into a sum of its parts and add and subtract fractions. At later grades students will learn algorithms for adding and subtracting fractions. Students will perform more complex analysis of data to look at mean, median, mode and range.
Asking a Question that gives Insight into learning
Promote learning/ push thinking As teachers we are not interested in our students ability to do what we have taught them to do. We are only interested in their ability to apply their newly acquired knowledge to a similar but different situation.
Asking a Question that gives Insight into learning How much longer was the longest wingspan from the shortest?
Understanding Place Value and Subtraction What does a student need to understand to use this process? What principals remain in place from subtraction with whole numbers?
Understanding Place Value and Subtraction What principals about subtraction doesnt the student understand?
Understanding Place Value and Subtraction What is going on in the diagram? Where do the numbers come from? Does this make sense?
Use of Formative Assessment Research suggested that attention to the use of assessment to inform instruction particularly at the classroom level in many cases effective doubled the speed of student learning. So, I sincerely hope that you take what weve learned, the tools we developed, and use the tasks this year to inform instruction.
Suggestions for Getting Started Have staff try some former tasks in classrooms and use staff meetings to use the Tools for Teachers to think about implications for instruction and design re-engagement lessons.