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Administrative Tools
• Comparison of Grade Level
• Graphs for Ethnicity, Home Language, Parent
Education, Gender, Language Fluency
• Description of test by standards, graphs by tasks
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Appendices
• NSLP Performance Levels
• Comparison of CST Levels to MARS Levels
• Correlations of STAR Scores to MARS Scores
• Correlations of CST Clusters to MAC Tasks
• Status of the Data
• Comparison of Raw Scores by District
• Audit Report by task and District
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Using Formative Assessment
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So the model that says learn while you ’ re in school, while you ’ re young, the skills that you will apply during your lifetime is no longer tenable. The skills that you can learn when your at school will not be applicable. They will be obsolete by the time you get into the workplace and need them, except one skill.
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The one really competitive skill is the skill of being able to learn. It is the skill being able not to give the right answer to questions about which you were taught at school, but to make the right response to situations that are outside the scope of what you were taught in school. We need to produce people who know how to act when they ’ re faced with situations for which they were not specifically prepared.
Seymour Papert (1998)
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It doesn ’ t matter very much which school you go to , but it matters very much which classrooms you ’ re in. In the US, the classroom effect appears o be at least four times the size of the school effect ( PISA,
2007 )
The greatest impact on learning is the daily lived experiences of students in classrooms, and that is determined much more by how teachers teach.
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“ teachers should not try to fit their teaching to each child ’ s style, but rather that they should become aware of different styles and help students also become aware of different styles and then encourage all students to use as wide a variety of styles as possible.
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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.
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• 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
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• The recognition of the profound influence assessment has on the motivation and selfesteem 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
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The teacher ’ s 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.
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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.
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Questions that give us insight into student learning are not easy to generate and often do not look like traditional test questions.
In the U.S. most teachers spend a majority of their lesson preparation time grading student work, and almost invariably doing so alone. In other countries much, if not the majority of lesson preparation time is spent planning how new topics can be introduced and which contexts and examples will be used, and teachers work in groups to devise questions to find out whether their teaching has been successful.
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Only 8% of the questions asked by teachers required the students to analyze, to make inferences, or to generalize. Less than 10% of the questions that were asked by teachers actually caused any new learning.
Only two good reasons to ask questions in class: to cause thinking and o provide information for the teacher about what to do next.
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How to provide constructive written feedback on the mathematics homework produced by their students - feedback included specific comments on errors, suggestions to students about how to improve and at least one positive remark. Students receiving constructive feedback learned twice as fast as control-group. Students given only comments scored on average 30% higher on work done in the next lesson than that done in the first.
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Students working logo enabled them to get a solution with little mental effort. For those using pencil and paper, working out the effect of a single rotation was much more time consuming, giving students an incentive to think carefully, and this greater
“ mindfulness ” led to more learning.
Students given the scaffolded response learned more and retained their learning longer than those given full solutions.
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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.
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Marco thinks
Plan C has a larger perimeter than Plans A and B. Explain why Marco is wrong.
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“ Marco probably counted. But he counted wrong.
”
“ How could this explanation be improved?
What is missing to make it convincing?
”
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“ 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?
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Jade sold only Peanut Butter Cookie
Dough. She raised $32. How many
Tubs did she sell?
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What do you think the student is doing?
What do the lines represent? What do the numbers represent? Does it make sense?
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This helps lay the foundation for proportional reasoning at later grades, for understanding input/output tables, for making graphs.
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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.
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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.
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“ 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.
”
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How much longer was the longest wingspan from the shortest?
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What does a student need to understand to use this process?
What principals remain in place from subtraction with whole numbers?
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What principals about subtraction doesn ’ t the student understand?
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What is going on in the diagram? Where do the numbers come from? Does this make sense?
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Consider the following from 5th grade:
She used 5/8 of the cooking oil.
and
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NCTM 2002 Yearbook - Making Sense of
Fractions, Ratios, and Proportions - gives tables on comparing whole-number multipliers and fractional multipliers.
Teachers need to ensure that they provide a variety of problem types.
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6th Grade - Rising to Meet CCSS
• Only 38% of the students met standards
• Task 1 - 38% scored 0 or 1 point (Rate
Concentrate) pick the juiciest for 1 point
• Task 2 - 18.5% scored 0 or 1 (Freezing in Fargo) could identify the lowest temperature
• Task 3 - 44% scored 0 or 1 (Fraction Match) complete addition equation
• Task 4 - 29% scored 0 or 1 (Lattice Fence) count the rhombi in a picture
• Task 5 - 51% scored 0 or 1 (Unfolding a Box) draw the unfolded box
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Preparing Students Who Think
No test can capture what is important for future progress: A fourth grade teacher who spends a great deal of time developing skills of independent and collaborative learning, who ensures that her students at solving problems, may find that her student scores on math are not as high as those who have emphasized only what is on the test.
And yet, the teacher who inherits this class will look very good because of the firm foundations that were laid in place.
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Which is the fruitier concentration?
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What do you think this student is doing?
What label could we attach to the division problem? How does this help us think about relationships?
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What is this student doing? Does it make sense? Why or why not?
10 > 6
Does this make sense? Why or why not?
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If teachers and teaching make the difference: then this tool is one of the most effective for changing practice. Lessons now available for sixth grade through geometry and can be placed into units of instruction. http://map.mathshell.org
Lessons, video, professional development
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• 7th Grade - Similar Figures - Evaluating
Statements about Length and Area
• 8th Grade - 200 Freestyle - Interpreting Time
Distance Graphs
• Geometry - Flip Sliding Away - Representing and Combining Transformations
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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 we ’ ve learned, the tools we developed, and do the tasks this year to inform instruction.
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• Test to CCST Standards – Have all 8 th graders take 8 th grade exam?
• Policy for 7 th and 6 th graders to match Smarter
Balance and state?
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