Analyzing Mastery And Re-Teaching Towards Mastery ① Analyze student scores A. Organize your data by type of problem and class mastery. ② Identify re-teaching strategies A. Determine why they chose the incorrect answers for the most prevalent mistakes. ③ Integrate re-teaching strategies A. Determine what structures or procedures you already have in place. B. Brainstorm what needed to be added or adapted. ④ Backwards plan the re-teaching strategies A. Ensure your assessment questions are valid. B. Develop a KUD (Know, Understand, Do) for every concept. C. Map the strategies on a calendar.
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Class Mastery Sample Data Learning(Goals Mastery Mastery Learning(Goal(1a Learning(Goal(1b Learning(Goal(1c Learning(Goal(1d Learning(Goal(2a Learning(Goal(2b Learning(Goal(2c Learning(Goal(2d Learning(Goal(3a Learning(Goal(3b Learning(Goal(3c Learning(Goal(3d Learning(Goal(4a Learning(Goal(4b Learning(Goal(4c Learning(Goal(4d Learning(Goal(5a Learning(Goal(5b Learning(Goal(5c Learning(Goal(5d Learning(Goal(6a Learning(Goal(6b Learning(Goal(6c Learning(Goal(6d Learning(Goal(7 Learning(Goal(8
37%
13%
25%
27%
33%
25% 7% 7%
33% 53% 40% 20% 7% 13% 20% 13% 13% 47% 27% 13% 40% 13% 40% 13% 40% 27% 13% 53% 13% 13% 20% 53% 7% 7%
A
B
C
D
33% 20% 7% 40% 40% 13% 20% 7% 13% 7% 27% 13% 13% 33% 0% 13% 7% 13% 13% 53% 40% 20% 20% 53% 33% 0%
33% 53% 20% 13% 7% 33% 13% 7% 20% 13% 7% 20% 40% 13% 13% 20% 40% 27% 33% 7% 0% 13% 20% 7% 40% 0%
20% 13% 20% 20% 27% 20% 20% 53% 27% 47% 20% 27% 20% 13% 33% 60% 20% 33% 33% 20% 13% 20% 40% 33% 7% 0%
7% 0% 40% 7% 13% 13% 20% 13% 20% 13% 27% 7% 0% 20% 40% 0% 7% 20% 13% 7% 40% 27% 7% 0% 7% 0%
question( number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
correct( Student( Student( answer 1 2 a b a b b b d d c c a b b c d d none c c none a d none c a none d c none c a none d a none c b none b b none d d b d a b a b c c b c d a b c a a a c a d b a c a b c a c a d b b 138.98 6.62 138.98 Count(of( Correct( 5 11 Answers Mastery 19% 42% Grade A F
Student( Student( Student( Student( Student( Student( Student( Student( Student( Student( Student( Student( Student( 3 4 5 6 7 8 9 10 11 12 13 14 15 c a c b d a b a b a b c a b b c a b c none b a b b b d a d c d b none d d c b b c d a a c a none a a c none d a a a b c a none c a c a b d a b c d b none a b c b d c b c b c a none d none a d a d c c c d b none c c c c d a c a c d b none c b c b c c c d b c c none d a b c d a a a c a d none d c c b b a b none d a c none c b none c none b c a b b b none c c b a a b d a a a b none c a d c d d c d d c c none c d c b c b c c c c c c b c a c none a b b b b b none d b c none b b d a a c c b d b c c d c a c c a b b c d b b a a c c a a c none a b d a d c d d a a a d a c d a b d c c d d b none a none a d a a b c a c c none b d c c c a c c c a a a a a b a b b a a c a b none b a d a none ;134.74 146.86 155.36 197.7 91.12 94.11 none 138.92 none ;135.26 none 5
24
7
7
6
22
5
0
4
6
8
8
5
19% F
92% F
27% A
27% F
23% F
85% F
19% B
0% F
15% F
23% F
31% F
31% F
19% F
Questioning the Validity of the Assessment Item • • • •
Was the question meaningful on its own? Were all of the choices plausible? Were all of the choices mutually exclusive? Was the question free from clues? – have grammar consistent with the stem. – are parallel in form. – are similar in length. – use similar language (e.g., all unlike textbook language or all like textbook language). Think back to what students got right and why they got it right!
Analyzing why students go the problem wrong or right • • • •
Was it the stem? Was it the answer choices? Was it the work they showed? Was it their decision making process? Adapted from: http://cft.vanderbilt.edu/guides-sub-pages/writing-good-multiple-choice-test-questions/
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Analysis of Learning Goals 100% - 80% Spiral in Homework Divide Decimals (90%)
79% - 70% Spiral in Do Now Surveys (77%)
69%-60%
59% or less
Small Group Instruction
Whole Class Reteach
Time Zones and Venn Diagrams
Intro to Algebraic Equations (52%)
Reading and Writing Numbers (90%)
(67%)
Divide Fractions (46%)
Solve Complex Equations (88%)
Add and Subtract Decimals (65%)
One-step Equations (44%)
Lines, Angles, and Polygons (85%)
Add and Subtract Fractions (65%)
Solve Ratios, Proportions and
Sequence Tables (81%)
Operations with Integers (65%)
Rates (44%)
Convert Units (63%)
Measures of Center (40%)
Symmetry and Transformations
Fractions, Decimals, and Percents
(63%)
(33%)
Graphs (60%)
Perimeter and Area (31%)
Coordinate Planes (60%)
3D Figures & Volume (31%)
Probability (58%)
Describe division (27%) Patterns and Function Tables (25%) Exponents (25%) Multiply Decimals and Fractions (23%) Properties of Operations (4%)
Error Analysis Learning goals
Error Analysis
One-step Equations
Guessed at an answer that is in the same fact
(44%)
family.
Patterns and Function
Applied the first found rule between terms
Tables (25%)
without checking that it is true for all terms.
Properties of Operations (4%)
Confused vocabulary with each other.
(31%)
Error Analysis Learning goals
Error Analysis
Describe division
Q16 – seemed to have just guessed. No
(20%)
work shown.
Q16 - split Divide Fractions
Q20 – divided across instead of flipping the
(24%)
second fraction
Multiply Decimals
Students didn’t apply the correct decimal place
Q20 - split
(23%)
to the final answer.
Operations with
Divide Fractions
Students divided across instead of flipping the
Integers (26%)
(46%)
second fraction and multiplying
Solve Ratios, Proportions and Rates (44%)
Students are using the conversion as an answer instead of applying the conversion.
Q21 – ignored the negative sign
Q21 – 39% chose C Measures of Center (26%) Q39 – split
Students are confused about what cube and
Q45 – 57% choose
square truly mean.
correct
Describe division
Students didn’t round up or round down given
Q51 – 26% choose A
(27%)
the context of the problem.
Q57 – 28% choose C
Fractions, Decimals,
Students did not convert the numbers in order
Intro to Algebraic
and Percents (33%)
to compare.
Equations (30%)
Exponents (25%)
formula as length times width.
Perimeter and Area
Students operating using measurements they
Q23 – 50% chose C
(31%)
didn’t need to use.
Q24 – 81% chose
3D Figures & Volume
Students didn’t recognize the base in the
correct
Q39 – didn’t put the data set in order Q45 – didn’t put the data set in order Q51 – didn’t put the data set in order Q57 – didn’t divide by the number of data points
Q23 – didn’t do the correct order of operations
K(now) U(nderstand) D(o) Learning Goal #1: Measuring Circles Students will KNOW… •
•
•
The formula for the circumference of a circle is πd, where π = 3.14 and d is the length of the diameter. 2 The formula for the area of a circle is πr , where π = 3.14 and r = the length of the radius. The formula for the volume of a sphere is ! 3 πr , where π = 3.14 and r = the length of !
•
•
the radius. The formula for the volume of a cylinder is 2 πr h, where π = 3.14, r = the length of the radius, and h = the height of the cylinder. The formula for the volume of a cone is ! 2 πr h, where π = 3.14, r = the length of the !
Students will UNDERSTAND… • • •
•
•
•
radius, and h = the height of the cylinder. •
•
•
There are four main parts of a circle: diameter, radius, center point and chord. The perimeter of a circle is called the circumference. A diameter is a straight line that crosses the center point of a circle and touches both sides of the circle. The radius is a line that starts at the center point of a circle and ends on the circle itself. The center point is a point inside of the circle that is the same distance from any point on the circle itself. The chord is a line with two end points on the circle, but doesn’t pass through the center point of the circle. Π is a special number for circles because it is the ratio of the circumference of the circle to the diameter of the circle. o Π is a constant number (always 3.14) because no matter the size of the circle, each point is always the same distance away from the center of the circle. To find the volume of a cylinder, find the area of the base and multiply that by the height. You take one third of the volume of a cone because the cone ends in an apex instead of another circle.
Students will BE ABLE TO DO… •
•
•
•
Calculate the circumference of circles. o Identify parts of a circle. o Identify diameter. o Plug lengths into formula appropriately. o Use the formula to calculate the circumference of a circle. Calculate the area of circles. o Identify the radius. o Plug lengths into formula appropriately. o Use the formula to calculate the area of a circle. Calculate the volume of a sphere. o Calculate the area of the base. o Describe how the area of the base relates to the volume of the figure. o Plug lengths into formula appropriately. o Use the formula to calculate the volume of a sphere. Calculate the volume of a cone and cylinder. o Calculate the area of the base. o Describe how the area of the base relates to the volume of the figure. o Plug lengths into formula appropriately. o Use the formula to calculate the volume of a cone. o Use the formula to calculate the volume of a cylinder.
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Cumulative List of Learning Goals Unit 1 Learning Goals (to be spiraled) 2 MC benchmark questions each = 12 questions 1. Read, write, and visually represent fractions.
Unit 4 Learning Goals (to be spiraled) 2 MC benchmark questions each = 12 questions
2. Read, write, compare, and visually represent fractions, decimals, and percents.
1. Use coordinate planes to draw functions and figures.
3. Add and subtract fractions.
3. Calculate probabilities.
4. Compute fluently with exponents.
4. Read, create, and evaluate basic graphs.
5. Add, subtract, and round decimals and whole numbers.
5. Compute and analyze measures of center in graphs.
6. Understand and apply the basic properties of operations.
6. Calculate elapsed time and read & create Venn diagrams.
2. Justify the bias and validity of generalizations made from survey data.
Unit 2 Learning Goals (to be spiraled)
Unit 5 Learning Goals (to be spiraled)
2 MC benchmark questions each = 10 questions
2 MC benchmark questions each = 10 questions
1. Recognize, extend, and create patterns using rules and function tables.
1. Classify, measure, and draw lines, angles, and polygons.
2. Multiply decimals and fractions.
2. Identify, describe, and apply congruence, rotational symmetry and transformations.
3. Describe and operate using quotative and partitive models of division.
3. Describe and calculate perimeter and area.
4. Divide decimals and represent remainders as decimals and fractions.
4. Compare and create mat plans and isometric representations from and for 3D figures.
5. Divide fractions and mixed numbers.
5. Convert within and operate using metric and customary units. Unit 3 Learning Goals (to be spiraled) 2 MC benchmark questions each = 12 questions 1. Read, write, and describe ratios, rates, and proportions. 2. Read, write, represent, and operate with integers. 3. Read and write numeric and algebraic equations, and use properties of operations with algebraic equations. 4. Evaluate one-step equations. 5. Read, write, and solve sequence tables. 6. Solve multi-step complex equations.
Unit 6 Learning Goals (new) 2 MC benchmark questions each = 10 questions 1. Consumer Math – better buys, Sales tax and discounts. 2. Calculate circumference and area of circles. 3. Calculate volume of cones and cylinders. 4. Calculate surface area.