PEDAGOGY

DATE: July 2006

TEACHER’S NAME: Nelda Clelland

TITLE OF LESSON: Using the Internet in support of developmental math instruction

SUMMARY: The purpose of this lesson is to explore technology-based resources and tools that can be used to bolster the math concepts taught in developmental math courses.

STANDARDS ADDRESSED: From Standards for Introductory College Mathematics Before Calculus: Mathematics as Problem Solving, Algebra, Statistics and Probability, Geometry and Spatial Sense, Measurement.

MATERIALS:

--Computers

--Flip chart

--Flip chart markers

--Handout

--Post-it notes

PART ONE: OVERVIEW

OBJECTIVES:

--Participants will explore relevant websites to find definitions of “numeracy”.

--Participants will explain the relevance of the definitions of numeracy to their own practice.

ACTIVITY:

--Participants brainstorm about the math they do every day. Write all suggestions on the flip chart. Find some common elements that relate to applying math in different situations. Participants visit two websites from the list on the handout and answer the handout questions. Participants share and discuss findings.

POINTS OF EMPHASIS:

--As instructors, we define “math” as classroom math but we acknowledge that the math we use is defined differently. So our learners don’t see the connection between what they are learning in class and what they need in life, either.

--This discrepancy between the math that we teach and the math that we need has led to the coining of a relatively new term that is presumed to encompass them both. The term is “numeracy” and a person who is “numerate” is able to make sense of the math of the classroom and apply it in various situations as needed.

PART ONE-A: USING CALCULATORS AND SPREADSHEETS

OBJECTIVES:

--Participants will explore websites and read relevant documents.

--Participants will relate positions on calculators and spreadsheets to their own practice.

ACTIVITY: Participants’ answers to the following questions are posted on the flip chart:

1) How many of you balance a checkbook using only a pencil and paper to do the math?

2) How many of you use a calculator when balancing your checkbook? How many of you have ever checked the addition in your checkbook, realized you made a mistake on a previous page, and wished you could just hit a button and correct all the entries at once?

--Discuss “pros” and “cons” of using calculators and spreadsheets in the adult math class.

--Review websites on handout and answer questions.

POINTS OF EMPHASIS:

--Our learners are no different than we are. They use calculators all the time. Spreadsheets would be a welcome tool to use in record keeping if they knew how to use them.

--There is a huge debate around the use of calculators in the adult math classroom. The “Back to Basics” group feels that kids and adults learning math should have to memorize the number facts and do the calculating without the assistance of a calculator. The “Progressive” group considers the calculator to be a tool just like any other that you use to make life simpler.

PART TWO: PROBLEM SOLVING

ACTIVITY: Participants write down ideas about their own school math experiences. Focus is on how information was presented to them, what they were expected to do with that information, and what happened after that. Participants share their recollections and try to find common experiences and relate them to the process of problem solving. Participants respond to the comment “You got the right answer but got it the wrong way”. Participants answer the question “What learning occurred in this situation for those who couldn’t do it the ‘right’ way?” Participants explore three websites on the handout from the perspective of a teacher planning a lesson and answer the questions.

POINTS OF EMPHASIS:

--Adults who come to developmental programs often were the ones who were told that they couldn’t do math because they couldn’t do it the “right” way.

--In the math classes they knew, no opportunity existed for exploring “other” ways to a solution. The focus is often on memorizing rules that would allow students to get the answers the “right” way. If you couldn’t remember the rules, you couldn’t be “good” at math.

--The challenge for adult educators is to change the structure of the math classroom so that the focus is less on getting the answer and more on the process of solving the problem.

--Math as problem solving rather than answer getting is much closer to the way we “do” math in real life.

--In everyday use, we frequently learn from our mistakes—so the process of problem solving must assume that mistakes will be made and it must articulate a way of dealing with them.

--In practicing the process of problem solving, we develop an assortment of problem solving strategies that we choose from, trying and selecting strategies until we find one that works. The most successful problem solvers are those that have experience with a wide range of strategies.

PART THREE: GEOMETRY, SPATIAL SENSE, AND MEASUREMENT

ACTIVITY: Participants generate a list of real life situations in which we use geometry, measurement, and spatial sense. Participants share ideas, decide if students should have a chance to generate such a list before beginning a lesson on geometry, spatial sense, and measurement, and justify their decision. Participants explore three websites on the handout and answer questions.

POINTS OF EMPHASIS:

--There is a disconnect between the math we learn in school and the math we use everyday. Learners frequently see no relevance between the isolated formulas of class and anything they need in life. Helping learners see the relevance helps them understand why they need the skill.

--Measurement is used in every facet of life but many adults have long forgotten the “rules”. Helping adults build understanding of measurement concepts makes the “rules” less important.

--Geometry helps learners analyze the characteristics of two- and three-dimensional shapes. Coordinate geometry teaches learners how to specify locations and describe spatial relationships.

--Measurement is a tool to be used in all of these investigations. Without a sense of measurement it’s impossible to make sense of space because there are not numerical benchmarks that have meaning.

--Geometry is useful in solving problems in other areas of mathematics and in real-world situations.

PART FOUR: DATA ANALYSIS, PROBABILITY, AND STATISTICS

ACTIVITY: Each participant checks his/her pulse by counting for 15 seconds and multiplying by 4 to get a pulse rate. Record each rate on a post-it note and put the notes on the wall. Tell them that the notes contain information. Ask “Is data information? How is it different from information?” Arrange the notes in rows, combining notes that have the same number. The result should be the equivalent of a rough bar graph. This illustrates that the pulse rates were just information when randomly placed on the wall. The rates became data when organized in a way that gives them meaning and significance. Participants explore three websites from the handout and answer the questions.

POINTS OF EMPHASIS:

--We are bombarded by information every day. Sometimes we need to organize that information in ways that make sense to us so we can use it. We use the term “data” to describe such organized information.

--We describe data in different ways—in charts, graphs, and tables—to accomplish different objectives.

--Interpreting information from charts and graphs is an important skill. Reading and interpreting graphic representations of data is also important in the workplace.

--One way to develop skill in interpreting charts and graphs is to get lots of practice creating charts and graphs. Such practice that focuses on topics of interest and relevance to learners makes the connection between real life math and classroom math more explicit.

PART FIVE: ALGEBRA

ACTIVITY: Ask participants if they use algebra in their own lives. Ask them for some examples and write responses on a flip chart. If participants draw a blank, offer some suggestions or guided questioning. Ask each person to name a pattern in their lives that involves numbers. Here are some examples: every weekday I drive 30 miles to work, every day I buy a newspaper, once a month I get a haircut. Ask each person to describe this common pattern using algebraic notation. Participants should be encouraged to work in pairs.

POINTS OF EMPHASIS:

--Adult learners don’t see any relevance in algebra and they resist having to learn it. Many adult educators don’t see the relevance either. An activity like the one just completed helps learners and educators see the relevance.

--Algebraic thinking is what we use to understand patterns, relationships, and functions; algebra is what we use to describe the patterns in terms others can understand and use.

--The value in being able to describe patterns algebraically is that doing so allows you to predict future patterns.

--With algebra, the learner uses mathematical models “to make predictions, draw conclusions, or better understand quantitative solutions.” (NCTM Principles and Standards for School Mathematics.)

--Algebra is a key to understanding the patterns of mathematics and the relationships among quantities.