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

Impetus

The 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-2B. 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. 6-8D. 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-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-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. 3-5C. 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

Research Questions

1. 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 & OperationsAlgebra

Geometry

Measurement

Data Analysis & Probability

Demographics

Sample

Snowball– 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

Rolen % n %

Median (Years) Range Median Range

Elementary 2 1.2% 2 100% 3 2 0.5 1Middle / JH School 38 22.6% 7 18.4% 14.5 36 1 15High School 64 38.1% 10 15.6% 14 37 2 17Career & Technical Ed 13 7.7% 3 23.1% 10 29 2 5Teacher Educators 32 19.0% 2 6.3% 19 38 0.5 5State or District Sup 15 8.9% 2 13.3% 14 40 2 7Curriculum Developer 2 1.2% 1 50.0% 27 4 2.5 5Other 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

0 20 40 60 80 100 120

None

General

College Algebra

Calculus

Statistics

48%

Reported familiarity with NCTM Standards

1 = No familiarity5 = Extremely familiarMedian = 2

Percent of your lessons containing instruction in mathematics?

0 10 20 30 40 50

OtherCurriculum developer

State or District SupervisorTeacher Educators

Career & Technical EdHigh School

Middle/JHElementary

Median Percent of Lessons Taught

“What percentage of mathematics in technology education should be below, at, or above the student’s current grade level?”

-20 -10 0 10 20 30Mean of Percentage Above Minus Percentage Below

ElementaryMiddle/JH

High SchoolCareer & Technical Ed

Teacher EducatorsSupervisors

Curriculum DevelopersOthers X

-9.1

Respondents’ Grade Level Assignments of NCTM Benchmarks

Greatest Success

74%

52%

54%

62%

0% 20% 40% 60% 80% 100%

N (6-8). Use factors

H (6-8). Model and solve problems

G (9-12). Represent translations

M (3-5). Fluency in adding

P-23-56-89-12College

Respondents’ Grade Level Assignments of NCTM Benchmarks

7%

11%

31%

30%

0% 20% 40% 60% 80% 100%

J (6-8). Rates of change

I (6-8). Predictions

A (9-12). Precision & Error

B (3-5). Congruence and similarity

P-23-56-89-12College

Least Success

Overall NCTM Benchmarks Grade Level Judgment Accuracy

0.45.5

21.7

40.1

22.2

9

1.205

1015202530354045

3 Under 2 Under 1 Under Correct 1 Over 2 Over 3 Over

%

Grade Level Judgment

63%

69%

74%

0% 20% 40% 60% 80% 100%

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

6%

7%

9%

0% 20% 40% 60% 80% 100%

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

0.1 2.2

14

42.2

27.5

12.2

1.705

1015202530354045

3 Under 2 Under 1 Under Match 1 Over 2 Over 3 Over

%

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

Implications

Replicate 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