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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10

 

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

Male

White

Crazy Hair

Lab Coat

Pocket Protector

Older

Eyeglasses

Symbols

Captions

Attributes

 

Math Trailblazers™


We then turned to an activity selected from the Math Trailblazers™ mathematics curriculum.  This elementary mathematics curriculum was developed to reflect the goals and standards of the National Council of Teachers of Mathematics.  It was developed with funding from the National Science Foundation by the TIMS™ (Teaching Integrated Mathematics and Science) Project at the University of Illinois.

The TIMS™ Laboratory method introduces children to the practice of science.

·         Identifying variables

·         Drawing Pictures

·         Organizing data in tables

·         Graphing data

·         Looking for and using patterns

 

The science in Math Trailblazers™ focuses on a small set of simple variables that are fundamental to both math and science:

·         length

·         area

·         volume

·         mass

·         time

 

Measurement is presented in meaningful, experimental situations. 

 

One such situation is exemplified by the Better “Picker Upper” unit from the Grade 3 curriculum.  This unit provides students with an example of how to integrate science into a mathematics unit.  In this series of activities students determine the absorbency of several different brands of paper towels based upon the area in square centimeters of the towel that is dampened by a fixed volume of liquid.

 

Exploration of this Math Trailblazers™ unit provided an introduction to...

 

·         design of an experiment

·         controlling variables

·         metric measure of area and volume

·         measurement of area of an irregular shape in square centimeters

·         estimating

·         fractions

·         numerical variables

·         creating bar graphs

·         reading bar graphs

 

 

Full Option Science System (FOSS)

 

We next explored a unit from the Full Option Science System (FOSS); a NSF funded elementary school science curriculum.  The goal of this activity is to further develop graphing skills and to explore integrating mathematics into a science curriculum. 

 

The "Lifeboats" unit from the FOSS curriculum is designed to develop scientific reasoning.  It further develops the concept of variable, and provides practice with conducting systematic investigations, gathering data and using it to make predictions, and graphing the result of investigations.  In “Lifeboats”, students create a fleet of paper cup boats of various heights and investigate the capacity of their boats in metric units, then graph the capacity of each boat in milliliters vs. the number of “passengers” (pennies).  They then use their graphs to predict the number of passengers that can be carried by another team’s boat.

Original Investigation

 

Finally, students engaged in open-ended inquiry of quantitative questions that they developed themselves using materials appropriate to the elementary science curriculum.

 

All of these activities model for prospective teachers the new standards in teaching science.  These standards emphasize that science should be taught as an ongoing process, based upon collaborative inquiry.

 

By the end of the semester, students had engaged in a series of related scientific investigations integrating quantitative reasoning into the science methods class and had

overcome some of their initial fear of “using” math and related skills in teaching science.  Students given the opportunity to develop quantitative skills in classes other than mathematics may be able to apply these skills more effectively in new and varied contexts.

 

 

This work has been further described in a manuscript “Quantitative Reasoning in an Undergraduate Science Education Course,” submitted for publication in The Journal of Mathematics and Science: Virginia Mathematics and Science Coalition.