miele

A New Emphasis on Quantitative Reasoning in a Science Education Course

Education 38 Education and Science/Mathematics and Technology

 

Eleanor Miele

 

School of Education

 

 

Quantitative reasoning has been defined as the process of interpreting and reasoning with quantitative information, and quantitative literacy as the ability to reason quantitatively.  A series of quantitative reasoning experiences were designed for the introductory course in math, science and technology education for undergraduate elementary education majors.  The activities are intended to integrate quantitative reasoning skills essential to elementary educators within the framework of a constructivist methods course.

 

At the undergraduate level education majors at Brooklyn College are currently required to take a series of science and science education courses.  All students take Core 7.1, Core 7.2, Core 8.1, and Core 8.2.  Education students also take the paired courses Education 38 and General Science 10, followed by Education 45 and General Science 20.  In addition, all education students take one of the following: General Science 9.1, 9.2, 9.3, and 9.4. 

 

Education 45 and General Science 10 are paired with courses in mathematics education: Education 45 and Math 1.97.  Students are typically under-prepared for the mathematics in these courses.

 

This discussion will focus on activities intended to develop quantitative reasoning skills in Education 38.


History of Education 38

 

Education 38 had been taught as an introduction to constructivist science education with an emphasis on science in society, including student and societal attitudes toward science and scientists.  A major goal of this course is to introduce students to the state and national standards which expect elementary school children to do science, not read, and listen to science facts.

 

The paired General Science course is an inquiry-based course.  It was originally intended to be offered by faculty in mathematics, the sciences and computer science.  Course topics reflect the expertise of the instructor.  In practice, the course is taught by faculty from the Departments of Biology, and Geology and a number of School of Education department adjuncts.  There have not been sections taught by faculty in mathematics or computer science in the last five years or more.

 

The general science course is overseen by a committee composed of representatives from the Departments of Physics, Biology, Chemistry, Geology, Mathematics and Education.

 

At a meeting of the General Science committee, it was identified as a goal to incorporate quantitative reasoning skills in each section of General Science 10, including at a minimum measurement, use of the metric system and graphing.  It was also suggested that introduction to pedagogical approaches to quantitative literacy be introduced in Education 38.

 

I had already identified introducing computer technology in pedagogy as a goal, including sessions on Internet research for teachers, children's educational software review and development of an Online course resource.

 

Now I faced the additional challenge of including an emphasis on quantitative skills.  

 

 

Quantitative Skills

 

The following quantitative skills, and their use in elementary school curricula, were identified as being essential to develop in the introductory educational methods course, especially in light of the fact that most of our students had not experienced this kind of learning as part of their own elementary school experience:

 

·         Formulating a testable question (hypothesis)

·         Understanding variables in scientific experiments

·         Categorical variables vs. numerical variables

·         Collecting and organizing data

·         Graphing data

·         Bar graphs vs. point graphs

·         Labeling axes

·         Fitting lines on point graphs

·         Predictions from point graphs: interpolation and extrapolation

 

The following will illustrate some of the activities I have introduced in recent semesters to emphasize quantitative literacy in Education 38, beginning with the Draw-A-Scientist Test.

 

 

 

 

 

The Draw-A-Scientist Test

 

The Draw-a-Scientist Test has been used throughout the educational community for years to help students identify their own negative stereotypes of scientists and those of their students.  I have used this technique for years to help students confront their stereotypes as a first step to overcoming their aversion to teaching science. Students are subsequently asked to research the lives of non-stereotypic scientists on the Internet and in children's literature.

 

This drawing illustrates a number of common negative or limiting stereotypes of

scientists held by typical Brooklyn College students.

 

Commonly Drawn Characteristics of Stereotypic Scientists

 

·         male

·         Caucasian

·         old

·         eyeglasses

·         "wild" hair

·         symbols of research - test tubes, flasks

·         captions - Eureka, e=mc2

·         lab coat

·         pocket protector

 

 

I wanted to introduce students to the idea that our collective responses to the Draw-a-Scientists test could tell us something about the frequency of certain stereotypes among students, that we had in fact collected some raw data that helped describe a population.  In order to use the data, we need to organize it and represent it in a useful way.

New standards in both science and mathematics education emphasize active participation in data collection, organization and analysis from the very earliest grades, including Kindergarten.  This work is often done collaboratively or collectively.  For instance, Kindergarten students may make a graph showing how the students in one class travel to school.  This might be a bar graph created by having each child place their name or a picture or icon on a collectively created graph.

 

Early Childhood Graphing

 

This pictograph was created using KidPix, a simple software tool commonly used in early childhood classrooms.

Organizing Data from the Draw-a-Scientist Test

 

In this activity, students identify the stereotypic features of their drawings by sharing their descriptions and noticing the common features.  Each stereotypic feature is then identified as one (categorical) variable that we can assess the (numerical) frequency of.  They then collectively create a bar graph representing the frequency of each stereotypic characteristic identified in their drawings.  Students are asked to come to the front of class and place one Post-it Note™  in each column if that characteristic is illustrated in their drawing.

 

The graph as it began to emerge indicated that students had not had sufficient experience creating even the simplest graphs to be ready to teach graphing even at the elementary school level.  However, students were able to recognize and correct the errors.

 

 

 

 

 

Frequency of Stereotypic Characteristics in Draw-a-Scientist Test

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Male

White

Crazy Hair

Lab Coat

Pocket Protector

Older

Glasses

Symbols test- tubes, etc.

Captions " " Eureka, etc."

 

Attributes

 

Working together, students revised their graph (see next page.)

 

In addition to using the graph to analyze the results of our research and discover the prevalence of limiting stereotypes, we were able to explore a number of pedagogical issues in childhood mathematics teaching.

 

Arithmetic concepts such as counting by groups, "counting on" and "counting back,"creating and simplifying fractions and calculating percentages were explored in context.  Prospective teachers were exposed to the power of using numbers in context to generate meaningful mathematical work in the classroom.

 

Final Graph of Data from the Draw-a-Scientist Test

 

Stereotypic Characteristics Illustrated in the Draw-a-Scientist Test

 

90%

95%

71%

71%

33%

67%

81%

71%

29%

 

19/21

20/21

5/7

5/7

1/3

2/3

17/21

5/7

2/7

 

19/21

20/21

15/21

15/21

7/21

17/21

17/21

15/21

6/21

 

19

20

15

15

7

14

17

15

6