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Mathematical Thinking for NJASK Presenter, Barbara VanDenBerg AMTNJ

Mathematical Thinking for NJASK Presenter, Barbara VanDenBerg AMTNJ. These are not long-term tests. This is the start of a 5 year cycle. Math Assessment Overview – cont’d. The NJ ASK is not a diagnostic test but a test to measure how well children are achieving the NJ CCCS

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Mathematical Thinking for NJASK Presenter, Barbara VanDenBerg AMTNJ

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  1. Mathematical Thinking for NJASK Presenter, Barbara VanDenBerg AMTNJ

  2. These are not long-term tests. This is the start of a 5 year cycle.

  3. Math AssessmentOverview – cont’d • The NJ ASK is not a diagnostic test but a test to measure how well children are achieving the NJ CCCS • Common misconception is that the NJDOE expects to have ten months of material taught in just over 6 or 7 months. This would be true if answering 27 out of 30 questions correctly equaled an “A” and so on, but that isn’t the case.

  4. Math AssessmentOverview – Grade 3 • 27 multiple choice items, which include 6 non-calculator multiple choice items • Each multiple choice item is each worth 1 point, the non-calculator items are each worth ½ point • Total points for multiple choice items is 24 • NJ ASK 3 contains a total of 30 items

  5. Math AssessmentOverview – cont’d • NJ ASK 4 contains a total of 37 items • 32 multiple choice items, which include 8 non-calculator multiple choice items • Each multiple choice item is each worth 1 point, the non-calculator items are each worth ½ point • Total points for multiple choice items is 28

  6. Math AssessmentOverview – cont’d • NJ ASK 4 contains 5 open-ended items worth 3 points each for a total of 15 points • Total points on the NJ ASK 4 is 43

  7. New Test Design 2008-? • Grades 5 and 6 will have a calculator inactive section (not a “computation section”) • Types of items: short constructed response (SCR), multiple choice (MC), and extended constructed response (ECR) • Mathematics testing is over two days with five sections (Grade 8 remains one day)

  8. Test Design Grades 5 and 6 • Day #1 Section #1, 8 SCR, 16 minutes, calculator inactive Section #2, 12 MC, 2 ECR, 35 minutes, calculator active Total Day #1: 51 minutes total testing time

  9. Day #2 Section #3, 10 MC, 1 ECR, 23 minutes Section #4, 10 MC, 1 ECR, 23 minutes Section #5, 10 MC, 1 ECR, 23 minutes Total Day #2 69 minutes total testing time, all sections on day #2 are calculator active

  10. Two day testing limits total testing time in one day SCR items to assess computation, estimation, structure, knowledge items, algebraic transformations, etc. SCR items limit amount of reading required of a child New Features

  11. New Features (SCR Items) • Each child starts with a section of Short Constructed Response Items (8/10) • NOT strictly computational items. • 2 minutes per item. • Answer is written in a 2” answer slot in answer folder • Human scored (0 or 1- no partial credit for work). There is flexibility in scoring- answer options, units, etc.

  12. New Features • Remaining four sections are a mix of MC and Extended Constructed Response (ECR) Items • MC Items (1.25/1.5 minutes) • ECR Items- 3 point maximum, human/rubric scored, 10 minutes • Increase in constructed response items and points (10 and 18/12 and 20)

  13. New Features • Grades 5&6 Have a Non-calculator Active Section • More Raw Score Points (50/52) • Each Content Cluster Receives an Extended Response Item (12 or 13/13) • Grades 5-7 Two Days of Mathematics Testing

  14. Hard Core Mathematical Facts • All ECR items are at the end of a section. • Generic answer slot for all ECR items, parts are gone and replaced with bullets. Answer does not have to be narrative. • Release items: 1 ECR item per grade with scoring rubric and exemplar papers; 1 SCR item per grade per year; and, 4 MC items per year with related statistics. • Measurements may be used to make conclusions.

  15. Hard Core Mathematical Facts • “Tick” marks will be used to show congruence as early as grade 5. • “Range” of data is a value. The range of 5, 9, 10, 4, 2, and 6 is 8 not “2 to 10”. • Probability- student may assume equally likely events. • 3x=36 is acceptable in grade 5.

  16. Cut Scores and Percents

  17. Sample SCR Items Grades 5 -7 Grade 5 Standard to be assessed 4.1.5 B.3 “Use an efficient and accurate paper-and pencil procedure for division of a 3-digit number by a 2-digit number.” Item: A gallon contains 128 ounces. Paul wants to divide 3 gallons of apple cider equally among the 2 dozen friends at his party. How many ounces of apple cider will each friend receive? (answer: 16) This standard cannot be assessed with a calculator active item. Nor could this standard be assessed with a multiple choice item as students could multiply the answer choices by 24 until they get 384.

  18. Grade 6 Standard to be assessed 4.4.6 B.2 “Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Item: A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. Arturo reaches into the bag and removes one marble. What is the probability that marble is red? (correct answers: .25, ¼, 5/20, or 25%) Note: SCR item allows a child to express the probability in the form they are most familiar with, not having to select from a form they may not be familiar with.)

  19. Teacher Concerns/Testing Notes • Measurements may be used to make geometric conclusions • Starting to use “tick” marks to show congruence at grade 5 • “Range” of data is a value. The range of 10, 12, 13, 26 is 16. • Probability- a student may assume equally likely events unless told otherwise. Items don’t use “draw” or “select.”

  20. Multiplication Symbols 5th grade 3x=36, (_)(_), x 6th and 7th grades 3x=36, (_)(_), x, dot • CPI’s are exhaustive • CPI’s across grades may be assessed at the lowest grade in which they occur

  21. Observations • Standard 1 – Estimation ex: 36 x 7 = 40 x 10. Students are rounding single digit numbers. • Standard 1 – Make sure students understand the difference between 3 groups of 4 and 4 groups of 3. • Standard 1 – Extend the use of fractions beyond pies, cakes and pizza slices (ie: containers being ½ full, ¼ full, etc.)

  22. Observations • Standard 2 – Make sure students are familiar with vocabulary of geometric objects (vertex – vertices). • Standard 2 – Students understanding of line(s) of symmetry • Standard 2 – Students need to understand the difference between perimeter, area, and volume.

  23. Observations • Standard 3 – Understand the properties of the arithmetic operations (commutative, identity) • Standard 3 – Concept of less than, greater than • Standard 3 – (grade 4) – Understand, NAME, and APPLY properties of arithmetic operations (commutative, associative, identity)

  24. Observations • Standard 4 (Graphing) – students are forgetting to give their graphs a label and title when prompted to do so. • Standard 4 (Graphing) – a very frequent error that students make is numbering the boxes instead of the lines (axes) on the graph. • Standard 4 (Graphing) – students need to be familiar with the different types of graphs (bar graphs, pictographs), reading tables. • Standard 4 (Graphing) – (4th grade) line plots, line graphs

  25. Observations • Standard 4 – probability vocabulary- more likely, equally likely, less likely, 1 out of 5, fractions (4th grade) • Standard 4 – simple counting (combination) situations involving charts, trees, diagrams • Standard 4 – Coloring a map • Standard 4 – Average (mean), most frequent (mode), middle term (median)

  26. Observations • Standard 3 –Patterns and sequences (grades 5-8) • Standard 4 – simple counting (combination) situations involving charts, trees, diagrams • Standard 4 – Coloring a map • Standard 4 – Vertex edge graphs

  27. SUMMARY • Students should answer every item • Have students use multiple approaches on multiple choice items • Students should attempt all parts of constructed response items- later parts may not be dependent on earlier parts. • Proficiency is not Perfection

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