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Prepared for the Professional Learning Community of Teachers of Mathematics by Dan Mulligan, September 2008

Empowering Each Student to THINK Research Strategies that Produce Learning for ALL. SESSION 2.

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Prepared for the Professional Learning Community of Teachers of Mathematics by Dan Mulligan, September 2008

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  1. EmpoweringEachStudenttoTHINKResearch Strategies that Produce Learning for ALL SESSION 2 "For as long as assessment is viewed as something we do ’after’ teaching and learning are over, we will fail to greatly improve student performance, regardless of how well or how poorly students are currently taught or motivated." Grant Wiggins, 1998 “Thinking is an engagement of the mind that changes the mind.” ~M. Heiddegar Prepared for the Professional Learning Community of Teachers of Mathematics by Dan Mulligan, September 2008

  2. Teacher/Learner Relationship “IDEAL teachers are individuals who see themselves as bridges over which students can cross, then, having facilitated their crossing, joyfully collapse, encouraging them to create their own bridges.” ~Kazantzakis

  3. Take a bow You are a principal • Please stand up if… You are left handed You have principles You balance your check book You have a twin You have traveled out of the continental U.S. this summer You teach hormonally charged children You teach while you are hormonally charged You provide school leadership You have children

  4. Workshop Goals • I will actively engage in building bridges within my grade-level and among other grade-levels; • I will join my team in exploring the research on student achievement (instruction + assessment) with a focus on math; • I will build my capacity to be an active member of a professional learning community; • I will increase my ability to embed 21st Century Skills into learning math standards; • I will have a good time learning and sharing… “Without continual growth and progress, such words as improvement, achievement, and success have no meaning.” ~Benjamin Franklin

  5. Learning Goals As a result of what we do today I will : create a story question involving fractions in the solution. solve a story question from one of my team members.

  6. When students know what they are learning, their performance, on average, has been shown to be 27 percentile points higher than students who do not know what they are learning.

  7. Main Myth about Learning Some part of the learner’s anatomy must be in contact with the chair in order for learning to take place!

  8. Collecting QUALITATIVE Data • Putting a Twist on the GLYPH method of collecting data: • Find the Glyph Page in your packet (yellow). • Create a team of 2 by using your team number and the following rule: • Even number match with next highest odd number (e.g., 2 &3, 4 & 5, 6 & 7, …) • Highest even number match with person number 1. • Interview your partner, using the categories from the next chart, to complete a Glyph OF YOUR PARTNER. • Share your completed Glyph with your partner. • Compare and contrast the 2 GLYPHS… How are they the same?How are they different?

  9. Checking for background knowledge: What is a hieroglyphic? • American Heritage Dictionary - hi·er·o·glyph·ic, adj.   • Of, relating to, or being a system of writing, such as that of ancient Egypt, in which pictorial symbols are used to represent meaning or sounds or a combination of meaning and sound. • Written with such symbols.

  10. Getting to Know YOU!!!

  11. Formative Assessment • Formative assessment is theprocess used by teachers and students during instruction that provides feedback to adjust teaching and learning for the purpose of improving student learning. Council of Chief State School Officers, October 2006 Notes: Process rather than a particular test…. It is not the nature of the test itself that makes it formative or summative…it is the use to which those results will be put.

  12. Importance of COMPREHENDING the question. RARE RARE Rrestate Aanalyze (what do you know that will help answer the question) Rrespond(answer the question) Eexplain(does your answer make sense?)

  13. Required pass rates foreach subgroup: 2005 tests – reading (65%) math (63%) 2006 tests – reading (69%) math (67%) 2007 tests – reading (73%) math (71%) 2008 tests – reading (77%) math (75%) 2009 tests – reading (81%) math (79%)

  14. The process of identifying and articulating similarities and differences among items. Comparing The process of grouping things into definable categories on the basis of their attributes. Classifying The process of identifying and articulating the underlying theme or general pattern in information. Creating Metaphors The process of identifying relationships between pairs of concepts (e.g., relationships between relationships). Creating Analogies What processes can students engage in to identify similarities and differences?

  15. Similarities and DifferencesAnalogies putter is to a set of golf clubs as 2 is to the set of primes 2, 3, 5, 7, 11, 13, … What is the common relationship? putter

  16. a. The number of cavities the sixth graders have? b. The number of people in the sixth graders’ families? c. The ages of the sixth graders’ mothers? d. The heights of the sixth graders in inches?

  17. ASKING the question in a VARIETY of FORMATS.

  18. What Works in Schools School Teacher Student 1. Guaranteed and Viable Curriculum 2. Challenging Goals and Effective Feedback 3. Parent and Community Involvement 4. Safe and Orderly Environment 5. Collegiality and Professionalism 6. Instructional Strategies 7. Classroom Management 8. Classroom Curriculum Design 9. Home Environment 10. Learning Intelligence/ Background Knowledge 11. Motivation

  19. Content-Related Evidence of Validity(Attained Curriculum) Essential Skills Essential Knowledge LEARNING TARGET (attained curriculum) Essential Vocabulary

  20. What does this look like in an effective K – 8 math program? Opportunity to LEARN – SOL 4.2 • Lessons are focused on the Essential KnowledgeDecimals and fractions represent the same relationships; however, they are presented in two different formats. Decimal numbers are another way of writing fractions. The base-10 models concretely relate fractions to decimals (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, money). • Learning is at the stated Essential Skill Represent fractions for halves, fourths, fifths, and tenths as decimals through thousandths, using concrete objects (e.g., demonstrate the relationship between the fraction 1/4 and its decimal equivalent 0.25).

  21. What is pi? What is the formula for circumference of a circle? Create a situation involving area of a circle. Essential Vocabulary Essential Knowledge Essential Skills

  22. “Learning from Explaining: Does It Matter if Mom is Listening” • Learning improves dramatically among young children who take the time to explain academic concepts to their mothers or who explain their logic aloud to themselves. • On a test of reasoning to 4 and 5 year olds: • Children who explained concepts to their mothers before taking a test scored correctly on 75% of questions; • Children who explained concepts aloud to themselves before taking a test scored correctly on 72% of questions; • Children who did not explain concepts at all prior to a test scored correctly on only 42% of questions; • The study examined youngsters’ ability to place toy insects in a certain pattern based on color and type. Breaden Research study completed in 2007

  23. Latoya and Kirk

  24. Latoya and Kirk LaToya – 159 cm Silk – 108 cm • 42 • + 135 • 177 • 108 • 69 • 73 • 4 cm below Shoulder – 135 cm Counter – 73 cm Stool – 42 cm

  25. Importance of EXTRANEOUS information in the question.

  26. Research on Imagery as Elaboration Students who used imagery to learn vocabulary, on average, performed # of studies

  27. The average student talks 35 seconds a day. The student who is talking is growing dendrites.

  28. Grade 6 Math Measurement & Geometry ISOSCELES TRAPEZOID 200 POINTS CONGRUENT CYLINDER 100 POINTS 100 POINTS PLANE FIGURE VOLUME TYPES of ANGLES 50 POINTS 50 POINTS 50 POINTS

  29. Grade 8 Math Patterns, Functions, & Algebra (32% of SOL test) COORDINATE PLANE 200 POINTS DEPENDENT VARIABLE DOMAIN 100 POINTS 100 POINTS FUNCTION LINEAR EQUATION FORMULA 50 POINTS 50 POINTS 50 POINTS

  30. YOUR TURN!!! 200 POINTS 100 POINTS 100 POINTS 50 POINTS 50 POINTS 50 POINTS

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