Instructional Systems & Learning Environments.
Below are two examples that showcase this key area. The first is a paper written for LT 726 in which I outline how learning styles reflect upon individual learner ability. The individual learner is the key to ensuring the success of every child in the classroom. The learning environment as well as the lesson preparation must incorporate knowledge of individual student needs to provide a comprehensive learning situation. While realizing that we cannot meet every whim and desire of the students, recognizing their unique learning ability and doing what we can ensures that each child will work up to the best of his or her potential.
The second is a collaborative set of math lessons created in conjunction with Cheryl Thaler and Betsy Koenig. Our goal with these lessons was to incorporate technology in a way that complimented many different learning styles. The different theories and models we reflected upon include Learning Styles, Constructivist Theory, Behavioral Theory, and Communities of Learning.
LT 726
July
15, 2002
By
Delesa Bosworth
The learning theory that I chose to reflect upon for this assignment is that of Learning Styles. As an ex-special ed. teacher, I truly believe that all students are smart in some ways; it’s just a matter of finding the style that is appropriate for the individual at hand. Traditional classroom experiences emphasize and reward students who function in very sequential and organized patterns. Less traditional learners are often left behind as they struggle to fit into predetermined molds that do not showcase their strengths.
Before I move into how I feel learning activities should be designed to reflect this learning theory, I will clarify that the Constructivist Learning theory is going to overlap quite a bit. In my way of thinking, the Constructivist Theory takes into consideration that learners all come to the same knowledge through their own style and that this is just one of many factors that must be taken into account when learning activities are designed.
According to the Learning Styles theory, information is gathered and understood differently by users. There are concrete and abstract perceivers, and active and reflective processors. The recommendations follow that all four different factors be considered when learning activities are in the design phase.
Technology can play an equalizing role at this point for the different types of children by creating learning tasks that are authentic and self-guided. By allowing the learners to control their own learning, they will follow through in a style that is suitable for them and allows them to create their own experiences. Their end products and assessments should showcase the conclusions that have been reached as well as how the information and knowledge that has been gathered is useful.
Students who require more of a hands-on type of approach to learning are thus able to form hypothesis to solve problems and use the technology available to them to prove or disprove their theories. Students need to work in settings that allow for discussion and collaboration with peers and sometimes experts to try out ideas and draw conclusions. This can be done through face-to-face interaction or via a distance through a variety of technologies.
Students need to have access to technology as a means of displaying their knowledge as well. Simple paper and pencil tests may not be able to showcase the entire learning and thinking process that students have worked through to draw their final conclusions. Some may still chose to write a final report in a word-processed form. Others, however, may choose to create presentations that incorporate visuals and auditory information. Their final product is a reflection of them as a learner and is acceptable when the teacher allows the students freedom to show that there is not one certain perfect answer that is being searched for.
I’m not saying that abstract learning and organization are not important. Instructional design just needs to take into account that there is more than one way to reach the final conclusion and to allow a wider variety of experiences to be explored during the process of learning. The technology available to us today in our classrooms allows us to let the learner be his or her own guide.
Developed By: Cheryl Thaler, Delesa Bosworth and Betsy Koenig
Dakota State University
LT 726 -Technology in the Curriculum
The Language of Algebra
Unit Goal: Students will understand the language of algebra
Grade level: 4-8
Lesson one title: definitions of math operations /naming of numbers
Purpose of this lesson: Students will use basic math definitions (sum, quotient, difference, product, operations) to rename numbers.
Activity procedure:
1) Working with partners, students will explore the site, www.amathsdictionaryforkids.com to define sum, quotient, difference, product, operations. We will use this site because it offers the definitions of the numbers in a colorful, basic manner, along with several examples of different ways the operation could be performed. It also offers students a hands on chance to apply the definition in an interactive, non-linear manner. Once the students have been given ample opportunity to explore and experiment with these applications, guide a class discussion to verify each of the definitions and its proper use.
2) For guided practice, in a large group setting, using a projection device and a calculator application, discuss as a class how numbers can be renamed. For example the number 15 could be stated as 5+5+5 or 16-1. The teacher, at this point, needs to explain to younger learners the use of logic while using a calculator for math applications. When using technology, one must keep in mind that 5x10 is not going to equal 500 and the user probably entered the equation incorrectly by hitting an extra zero. The user must always stay alert during the data entry process and reason through the answer given to determine if it is logical or not.
3) Allow for independent practice by placing students in small groups. Students will use calculators to perform addition, subtraction, multiplication and division to rename numbers. The calculator allows the students to perform the functions more rapidly and encourages further experimentation. Teacher will circulate through the groups and facilitate by asking “what if” questions. “What if you change that to an addition problem?”
4)
Assessment: Each group will produce 5 examples created using the
calculators to rename one number. They will present the examples aloud to the
class and by writing them on the projection device. Students need to record the
different renamed numbers for tomorrow’s lesson. Note: It is anticipated that
students will use more than one operation, which will lead to tomorrow’s
discussion of order of operations. Ex. 5x2+3=13
uses both multiplication as well as addition. An example of what could be handed
in follows.
The number the team chose to be
renamed is 15. Some of the possible
examples are 5+5+5, 5+10, 30/2, 5*3, 17-2, etc. All of these examples will are different ways of stating the
number 15.
Reflection Paragraph: Learning Styles
We chose the website as a means of defining the algebra terms over simply looking them up in a glossary as this web site provides not only a definition to the term, but also examples and opportunity for the learner to try out the method making it much more concrete for some learners. The projection device allows the teacher an opportunity to demonstrate the use of the calculator to the entire class in a means that is large enough for all of the students to view at one time. This is opposed to trying to use a regular calculator for a class demonstration. Students will work in small groups for this lesson to allow discussion and to stimulate creativity when producing their renamed numbers. We want the students to feel free to “play” with the numbers and ask “what if” questions to discover how they can change different variables (a term that will be defined in later lessons) and operations and still end with the same the final number. The calculators will provide them freedom to try out many different operations and discover how many different operations can be used to rename one number. Abstract learners will gather information from the definitions gleaned from the first website visited. Concrete learners will be given time to apply the information gathered during the experimentation time with the calculators. Using various learning styles, students will become more rounded thinkers.
Lesson title two: order of operations
Purpose of the lesson: Students will demonstrate and reflect upon how the sum, quotient, difference or product of numbers are affected by the order of operations.
Activity procedure:
1) In large group, orally review definitions learned in lesson one
2) In a computer lab, as a large group, open excel and explain to students that a spreadsheet performs calculations
3) Students individually open excel and in cell A1 type 5+10*2 (it should equal 25)
4) then in cell B1 type (5+10) *2 (this should equal 30)
5) A handout will be given to students to continue their discovery exploration. They may do the spreadsheet exercise in this handout in dyads. (See Lesson 2 – handout attachment)
6) As teacher facilitates, students will continue to put the numbers and expressions as in the handout in their spreadsheet. They should begin to question the difference in the answers, between using the parenthesis and the different order in which the data is input. Allow time for students to do the handout in Excel and discover and generate responses that explain the differences.
7) Draw students’ attention back to large group setting and using a projection device, provide more examples that demonstrate how the order of operations affect the result.
8)
Assessment: Each dyad will write and present a reflection based on
what they discovered in this lesson (The order of operations according to how
they understand it). In order to present their reflection to the class, each
group will assume the role of teacher by using the projection device.
The group will demonstrate, using Excel, the order of operations.
These reflections will determine need for re-teaching and drill and
practice.
Reflection Paragraph: Constructivist Theory
All three of us are math teachers and wanted to use the constructivist theory to teach it. Math is generally taught as teacher-centered. We wanted to experiment with reflections, discovery learning, and alternative assessment in teaching math, successfully. The spreadsheet was chosen as our technology choice because it always follows the rules of the order of operations regardless of how the data is entered. The large group setting in this lesson is used to give all students general instruction. Dyads or pairs are also used to give all students a chance to socially think things out and dialog together as they discover for themselves the rules to the order of operations.
Purpose of this lesson: Students will correctly use placeholders (variables) in algebraic expressions.
Activity procedure:
1) Students will individually explore the site, (revisit this previously used site) www.amathsdictionaryforkids.com to define missing number, placeholder (variable), expression
2) Individually in a lab setting, give students a detailed instructional handout (included in attachments) for entering specific numbers in cells and to add these numbers using cell references as variables (placeholders). Example: in cell A1, put 1, in cell B1 put 2, in cell C1, put 3 and add them in D1, but use one cell reference instead of numbers so you have D1=A1+2+3,
3) For independent exploration, have students change numbers in A1 and see the results change in D1 according to the changes
4)
As a lesson extension, increase example complexity to adjust to
students’ needs. Use B1 and C1 as cell references (variables) and change these
and view the change in D1.
5) Assessment: Students will print out and hand in their spreadsheet created according to the handout for the instructor to grade and see if each student has learned the basics of variables and expressions. The student will also give an example of an expression using cell references as variables, which will be handed into the instructor as well.
Reflection Paragraph: Constructivist Theory
Just as in lesson 2 we want to give our learners a choice in their math instruction making them the center of their learning and the teacher the facilitator. We chose the spreadsheet because it visually demonstrates how changing a variable within the expression affects the result. The students will be following the Constructivist Theory of learning again as they will be relying on their previous knowledge of mathematical equations to discover what affect changing variables will have. This knowledge will build upon the knowledge gained from the previous lesson. The student is working as an individual on this problem in a computer lab setting. This concept is very important to mathematics each student needs to be evaluated on his or her own understanding.
Lesson four title: Properties
Purpose of this lesson: Students will identify the commutative, associative, identity, multiplicative and distributive properties.
Activity Procedure
1) In a large group setting in the computer lab, introduce properties using the web site http://www.aaamath.com/pro.html. Students will visit the web site on individual computers as the properties are defined.
2) In the same setting, the teacher will demonstrate how to use http://www.aaamath.com/pro.html via the projection device. The teacher will scroll through the presented information to the orange box with the start button. Then click on “Start” for an expression to appear. The teacher and students will discuss which property is displayed. The teacher will then click on the button indicating the property. The teacher should work through examples, until each property has been displayed.The teacher will show the students where the answer appears, the number of correct answers and the number of incorrect answers and the percentage of correct answers.
3) On an individual basis, students will visit the website http://www.aaamath.com/pro.html to practice identifying properties.
4) Assessment: Using the above website, students complete 10 exercises of addition and 10 exercises of multiplication and print results and give the results to the teacher. The results will determine re-teaching.
Reflective paragraph: behavioral theory
We chose to use this website for our technology as it provided introduction to the theories followed up by hands-on practice. This follows the Behavioral Learning Theory as the students practice identifying the correct property. Since the students are rewarded for correct answers, we felt that students should work individually in order to receive personal satisfaction in earning correct responses. They are rewarded with a correct answer comment or given the correct answer if necessary. Their percentage score reflects how many exercises are answered correctly.
Lesson five title: Variables and equations
Purpose of this lesson: Students will write algebraic equations for real life situations.
Activity Procedure:
1) In the computer lab, visit the website http://www.mathgoodies.com/lessons/vol7/expressions.html as a class. Read information aloud to class. Click on links for definitions. Explain that the variable is what you are trying to find (the unknown).Together create equations to solve the 5 examples. Students will independently complete practice problems found on this site. If students chose an incorrect answer, they will need to determine another answer, as the site doesn’t give the correct response immediately. This gives the student time to get comfortable with writing equations at his/her own pace before being placed in a group setting to write equations.
2) In a large group setting, show the short teacher created Quick Time video that demonstrates real life applications of simple algebra equations. This video opens with a teacher and student looking at an algebra assignment. The student makes the comment “Why do we have to learn this stupid algebra? I’ll never use it anyway.” Five situations where algebra is used are presented. This first is a man and his St. Bernard in a pickup. The posed question is how far can Joe and his St. Bernard travel on a tank of gas. The second situation is mixing herbicide and determining the amount of water to be used. The third situation is determining total wages given amount per hour and total hours worked. The fourth situation is the total cost of 10 brownies, given the cost of one brownie. The last situation is determining the total cost of purchasing soda pop, candy and a candy bar. Note: We’ve tried inserting the video onto a webpage and it doesn’t work. We do have the video on a CD.
3)
An example
PowerPoint of what the students are expected to create will be
shown.
4) Assessment: In small groups, students will create a PowerPoint (3-4 slides) for one real life application presented in the video. The groups will chose which of the presented applications from the video they wish to solve. They are placed in groups in order to work cooperatively. All students in the group are expected to contribute to the presentation. Since the requirement is 3-4 slides, students can take turns creating slides. The students will assume the teaching role and present their equation to the rest of the class and explain how they set up the equation. Using Powerpoint allows the students to easily share their presentations on a projection device. The slides will demonstrate the students’ knowledge of setting up the algebraic equations, using the variable correctly, and solving the equation. All PowerPoints will be combined together for one presentation.
5) Lesson extension: Allow students to visit the web site http://www.aaamath.com/equ.html to review the order of operations and solving equations.
Reflection Paragraph: Communities of Practice
We chose the Math Goodies web site to introduce this unit and give the students a feel for how algebraic applications relate to real life situations. They are given examples of how the real-life situations are translated into equations incorporating variables for the missing components. The video gives the students ideas for applying these applications to their own situations. The PowerPoint Presentations allow students to demonstrate the entire process of defining the problem, identifying the proper application for the situation, creating an equation representing the situation, and finding a solution. The Communities of Practice Theory suits this lesson as the students work as teams to create the Power Point showing the algebraic equations. The separate group presentations are combined to create one final collaborative effort for a final product of the whole unit.
Lesson 2 – Spreadsheet For Order of Operations
Directions: Type the following expressions in the specified cell. (Do not type the “quotation marks”) When using a spreadsheet or any computer application the symbol that tells the computer to multiply is the * (asterisk- shift and the numeral 8)
In cell A1 type “=5+10*2” In cell A2 type “=18+1*2”
In cell B1 type “=(5+10)*2” In cell B2 type “=(18+1)*2”
In cell C1 type “=10+10/2” In cell C2 type “=2+0*5”
In cell D1 type “=(10+10)/2” In cell D2 type “=(2+0)*5”
In cell E1 type “=8*1+2” In cell E2 type “=111/11+6”
In cell F1 type “=(8*1)+2” In cell F2 type “=(111/11)+6”
In cell G1 type “=16/4+5”
In cell H1 type “=(16/4)+5”
In the blanks below think about how the spreadsheet solved the expressions, write the rules for the order of operations. Print out the resulting spreadsheet and turn it in, staple this with your completed reflections to the back of your printed spreadsheet.
Lesson 3- Spreadsheet Handout- Variables
Set up a spreadsheet like below:
A B C D
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1 |
2 |
3 |
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4 |
5 |
6 |
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7 |
8 |
9 |
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In cell D1 type the formula “=A1+2+3” change the contents of cell A1 and press enter and see what happens in cell D1.
In cell D2 type the formula “=4+B2+6” change the contents of cell B2 and press enter and see what happens in cell D2.
In cell D3 type the formula “=7+8+C3” change the contents of cell C3 and press enter and see what happens in cell D3.
In cell E1 type the formula “=A1+B1+C1” change the contents of cells A1, B1 and C1 and see what happens in cell E1.
In cell E2 type the formula “=A2+B2+C2” change the contents of cells A2, B2, and C2 and see what happens in the cell E2.
In cell E3 try this—type “=D1/B1 and see what you get in cell E3.
Try more of these. You will hand in the print out at the end and you will be graded. Do you see how changing a number in a placeholder (in this case we are using cell references) or variable you can change the result of the expression?
Write down some examples of your own equations using cell references as variables.