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Judgments of Mathematics Grade-Level in Technology
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Judgments of Mathematics Grade-Level in Technology Jim Flowers Mary Annette Rose Ball State University This research was supported in part by funding from the Council on Technology Teacher Education. Location: HTTP://jcflowers1.iweb.bsu.edu/pres/math.pdf
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Judgments of Mathematics Grade-Level in Technology. Jim Flowers Mary Annette Rose Ball State University. This research was supported in part by funding from the Council on Technology Teacher Education. Location: HTTP://jcflowers1.iweb.bsu.edu/pres/math.pdf. Impetus. The STEM movement - PowerPoint PPT Presentation
Transcript of Judgments of Mathematics Grade-Level in Technology
Judgments of Mathematics Grade-Level in Technology
Jim FlowersMary Annette Rose
Ball State UniversityThis research was supported in part by funding from the Council on Technology Teacher Education.
Location: HTTP://jcflowers1.iweb.bsu.edu/pres/math.pdf
ImpetusThe STEM movement
– Fragmentation / uncoordinated elements of STEM fields– “Integrating the appropriate levels of mathematics and science
into instructional content” (94% agreed, Wicklein, 2007, p. 13)
TEE teachers preparation to apply mathematicsExamples of below-grade mathematics
“Sure, the juniors and seniors in my classes use math. They have to submit a bill of materials, and that requires plenty of multiplication and addition.”
National Council of Teachers of Mathematics (NCTM) Standards
How familiar are
you with the NCTM
Standards?
What grade level is this NCTM expectation?
1. “Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute”
A. P-2B. 3-5C. 6-8D. 9-12E. College
GradeLevels
What grade level is this NCTM expectation?
1. “Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute”
A. P-2
B. 3-5C. 6-8D. 9-12E. College
What grade level is this NCTM expectation?
2. “Analyze precision, accuracy, and approximate error in measurement situations”
A. P-2B. 3-5C. 6-8D. 9-12E. College
What grade level is thisNCTM expectation?
2. “Analyze precision, accuracy, and approximate error in measurement situations”
A. P-2B. 3-5C. 6-8
D. 9-12E. College
What grade level is the math in this technology learning activity?
3. “Numerically Controlled (NC) Mill Problem: Engraving your Name. Step 1. Plot the first letter of your name on an x/y coordinate grid and label the coordinates of the key points.”
A. P-2B. 3-5C. 6-8D. 9-12E. College
What grade level is the math in this technology learning activity?
3. “Numerically Controlled (NC) Mill Problem: Engraving your Name. Step 1. Plot the first letter of your name on an x/y coordinate grid and label the coordinates of the key points.”
A. P-2
B. 3-5C. 6-8D. 9-12E. College
What grade level is the math in this technology learning activity?
4. “Now that you know your vehicle's time-trial speed, determine how far your vehicle would travel at that speed if it ran for one minute.”
A. P-2B. 3-5C. 6-8D. 9-12E. College
What grade level is the math in this technology learning activity?
4. “Now that you know your vehicle's time-trial speed, determine how far your vehicle would travel at that speed if it ran for one minute.”
A. P-2B. 3-5
C. 6-8D. 9-12E. College
Research Questions1. How familiar are technology educators with the NCTM
standards? 2. How accurately do technology educators identify the grade
level associated with NCTM benchmarks (i.e., “expectations”)?
3. Given examples of mathematics in technology education, how accurately do technology educators identify the mathematics grade level (with NCTM benchmarks as the standard)?
4. Are there differences among technology educators in terms of their ability to correctly classify NCTM expectations and mathematics in technology education?
Methods: Math in Technology Activities
Document ReviewThe Technology & Engineering TeacherTech DirectionsEngineering by Design
Researcher examples
40 Word Problems
Independent CodingLicensedPracticing Math TeachersUsing NCTM Standards
Methods: Survey Instruments
15 Word Problems100% Grade-Level AgreementBroad coverage of NCTM StandardsBroad coverage of Technology
15 Items: NCTM Expectations3-5 6-8 9-12
Numbers & Operations
Algebra
Geometry
Measurement
Data Analysis & Probability
Demographics
SampleSnowball– CTTE List Serve– ITEA Council of Supervisors– ITEA State Associations List– Request in STEM Connections
Online Survey– Open for 3 months– Fall 2011
Sex, Teaching Experience, Engineering Courses Taught
Respondents Female
Teaching
Experience K12 Engineering Courses Taught
Role n % n % Median (Years) Range Median Range
Elementary 2 1.2% 2 100% 3 2 0.5 1 Middle / JH School 38 22.6% 7 18.4% 14.5 36 1 15 High School 64 38.1% 10 15.6% 14 37 2 17 Career & Technical Ed 13 7.7% 3 23.1% 10 29 2 5 Teacher Educators 32 19.0% 2 6.3% 19 38 0.5 5 State or District Sup 15 8.9% 2 13.3% 14 40 2 7 Curriculum Developer 2 1.2% 1 50.0% 27 4 2.5 5 Other 2 1.2% 1 50.0% 9.5 3 2 0
TOTAL 168 100% 28 16.7% 15 40 1.5 17
Years of High School Mathematics Courses Successfully Completed
1%2%
8%
23%
53%
13%0
1
2
3
4, No AP
4, AP
Participants: College Mathematics
McAlister (2005) reported4 of 24 programs required calculus
None
General
College Algebra
Calculus
Statistics
0 20 40 60 80 100 120
48%
Reported familiarity with NCTM Standards
1 = No familiarity5 = Extremely familiarMedian = 2
Percent of your lessons containing instruction in mathematics?
Other
Curriculum developer
State or District Supervisor
Teacher Educators
Career & Technical Ed
High School
Middle/JH
Elementary
0 5 10 15 20 25 30 35 40 45 50
Median Percent of Lessons Taught
“What percentage of mathematics in technology education should be below, at, or above the student’s current grade level?”
-15 -10 -5 0 5 10 15 20 25 30Mean of Percentage Above Minus Percentage Below
Elementary
Middle/JH
High School
Career & Technical Ed
Teacher Educators
Supervisors
Curriculum Developers
Others X
-9.1
Respondents’ Grade Level Assignments of NCTM Benchmarks
Greatest Success
N (6-8). Use factors
H (6-8). Model and solve problems
G (9-12). Represent translations
M (3-5). Fluency in adding
0% 20% 40% 60% 80% 100%
52%
54%
62%
74%
P-23-56-89-12College
Respondents’ Grade Level Assignments of NCTM Benchmarks
J (6-8). Rates of change
I (6-8). Predictions
A (9-12). Precision & Error
B (3-5). Congruence and similarity
0% 20% 40% 60% 80% 100%
7%
11%
31%
30%P-23-56-89-12College
Least Success
Overall NCTM Benchmarks Grade Level Judgment Accuracy
3 Under 2 Under 1 Under Correct 1 Over 2 Over 3 Over0
5
10
15
20
25
30
35
40
45
0.4
5.5
21.7
40.1
22.2
9
1.2
Grade Level Judgment
%
0% 20% 40% 60% 80% 100%
63%
69%
74%
P-23-56-89-12College
Find the impedance Z of a circuit with 20W of reactance XL represented by the vector diagram.
A twin-engine airplane has a speed of 300 mi/h in still air. Suppose the airplane heads south and encounters a wind blowing 50 mi/h due east. What is the resultant speed of the airplane? To solve, find the sum of the vectors that represent the speed of the airplane and the speed of the wind.
Now that you know your vehicle's time-trial speed, determine how far your vehicle would travel at that speed if it ran for one minute.
Respondents’ Grade-Level Estimates of Math in Technology Activities
Greatest Agreement
Respondents’ Grade-Level Estimates of Math in Technology Activities
Least Agreement
0% 20% 40% 60% 80% 100%
6%
7%
9%
P-23-56-89-12College
After using a Boyle's Law apparatus or computer simulation to collect pressure and volume readings, students "create a graph from the data collected, with the 'y' axis being Volume and the 'x' axis being Pressure.
Numerically Controlled (NC) Mill Problem: Engraving your Name. Step 1. Plot the first letter of your name on an x/y coordinate grid and label the coordinates of the key points.
One step in completing the flexural test of a panel is to plot your findings on a data table. "Plot the weight (W) on the abscissa (x coordinate) and the sag (S) on the ordinate (y coordinate).
Overall Grade-Level Estimates of Math in Technology Activities
3 Under 2 Under 1 Under Match 1 Over 2 Over 3 Over0
5
10
15
20
25
30
35
40
45
0.12.2
14
42.2
27.5
12.2
1.7
Grade Level Judgment
%Overall: 4.6 more overestimates than underestimates per respondent for 12 items
Conclusions
How familiar are technology educators with the NCTM standards?
Reported familiarity = 2 of 5, somewhat unfamiliar
Corroborated by Assignment
How accurately do technology educators identify the grade level associated with NCTM expectations?
Average accuracy = 40%
Range of 7% to 74% accuracy of 15 sample expectations
Overestimates mirror underestimates
Given examples of mathematics in technology education, how accurately do technology educators identify the mathematics grade level?
Average accuracy = 42% agreement with coders
4.6 more overestimates per person than underestimates
Are there differences among technology educators in terms of their ability to correctly classify NCTM expectations and mathematics in technology education?
Some groups had small n
No differences found among groups
ImplicationsReplicate with a representative sample.
Replicate with Common Core standards.
Technology & Engineering teachers could be assisted in aligning the math in their courses with existing math standards (NCTM & Common Core).
Judgments of Mathematics Grade-Level in Technology
Jim FlowersMary Annette Rose
Ball State UniversityThis research was supported in part by funding from the Council on Technology Teacher Education.
Location: HTTP://jcflowers1.iweb.bsu.edu/pres/math.pdf
