Wednesday, May 23, 2012

Constructivism in Practice


This week we were asked to discuss how the instructional strategy, generating and testing hypotheses, correlates to the constructivist and constructionist learning theories.  Before addressing this correlation, it is necessary to first discuss these two learning theories.

Constructionism and Constructivism are terms that are often used interchangeably in the schools in which I have worked or volunteered.  If you were to conduct a search online for one of these terms, you will also get numerous hits for the other as well.  The reason is because these two learning theories are closely related to one another.  “Constructionism builds on the Constructivist Theories of Jean Piaget, asserting that knowledge is not simply transmitted from teacher to student, but actively constructed in the mind of the learner.  (Orey, 2001)  Both learning theories state that learning takes place, and connections are made when students are actively involved in an activity, but the constructionist theory goes a step farther and states that, “Ideas are more likely to be created when learners are actively engaged in building some type of external artifact that they can reflect upon and share with others.  (Orey, 2001)

I believe in these two learning theories and I try to conduct lessons based on these models.  Think back to your school days?  What are some of the things you remember learning about?  I always remember the big projects, the science fair projects that I spent countless hours on, or the wooden end table I made and everything that had to be done to make it correctly.  The projects that stand out in my mind were the ones in which a great amount of my time had been invested, striving to find my own answers and make a display or object to demonstrate what I had learned.  These projects incorporated numerous subject areas and the knowledge I gained has stayed with me always. 

Generating and testing hypotheses is very similar to the constructivist and constructionist learning theory.  It too, involves putting the students in the driver’s seat, so to speak.  It allows them to generate a question or hypothesis, and then actively research to support or decline their original hypothesis (Pitler, Hubbell, Kuhn, & Malenoski, 2007).  As they research they are strengthening connections in their brain, helping them to really understand the task at hand.  Even though their hypothesis may be wrong, students will discover this on their own and have an understanding why, instead of just getting feedback from their teacher, and being left to wonder why the hypothesis was incorrect.   Learning that one’s initial thoughts were incorrect causes a disequilibration for the student.  (Laureate Education, Inc., 2010).  The student must then alter their thinking processes in order to make sense of the new material and to understand it fully. 

Technology can really facilitate the testing hypothesis process.  The Internet is a wealth of resources including text, video, and even the capabilities to chat with experts in a field.  Technology can also help students to organize the data they have collected.  In our text, Using Technology with Classroom Instruction that Works, it discusses how the use of spreadsheets can be a beneficial data collection tool.  Spreadsheets allow for students to organize their data and to manipulate it with ease.  It allows for students to use features such as the formula feature to complete computations, allowing students to focus on other aspects of the activity instead of the tedious computations.  It also increases accuracy with answering computations, increasing the likelihood that students’ revised hypothesis will be accurate since the calculations will likely be free from error (Pitler, et al, 2007). 

Technology can also be used to participate in simulations.  “Students can see the outcome of their hypotheses, often in virtual situations that would be impossible or financially unfeasible in real life” (Pitler, et al, 2007).  Although it does take some time to search to find the simulation that really meets your needs, “simulation software also can provide incredibly engaging learning environments, resulting in increased motivation and retention in learning” (Pitler, et al, 2007). 

One simulation I have explored briefly with my high ability students this year is http://mathbydesign.thinkport.org/.  It is a simulation that allows students to create a park or an environmental center.  There are a number of tasks that must be completed, such as determining the location for the concession stands based on certain criteria.  Although this simulation is higher level and challenging for the majority of the grade, my high ability students loved the challenge and often asked to play the game in their free time. 

Another site I found was http://www.explorelearning.com/.  This site has over 450 math and science simulations for grades 3-12.  This site does require a paid membership but it does offer a great free 30-day trial period. 

The instructional strategy, generating and testing hypothesis really reflects the key components of the constructivist and constructionist learning theories.  It allows for students to be an active part of their learning experience.  The teacher’s role is to act as a facilitator and provide guidance to the students to help them successfully reach their own conclusions.  Generating a hypothesis is focusing on the big picture, or is similar to the top-down model.  Instead of learning each component and then understanding how they fit into the big picture, the students are focusing on the main topic while experiences the subtopics along the way.  The main component of each of these is that the students are constructing their own understanding of the material, making neural connections, increasing the likelihood of students retaining the content. 


References

Laureate Education, Inc. (Producer). (2011). Program seven: Constructionist and constructivist learning theories [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from http://laureate.ecollege.com/ec/crs/default.learn?CourseID=5700267&CPURL=laureate.ecollege.com&Survey=1&47=2594577&ClientNodeID=984650&coursenav=0&bhcp=1

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. Retrieved from http://projects.coe.uga.edu/epltt/index.php?title=Main_Page

11 comments:

  1. Great idea on the simulation for the higher level students. It is difficult to find activities that engage them and challenge them. I wish I could find something similar for higher level language arts students. Do you have any ideas? Thanks!

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  2. Mary
    I think language arts would be the most difficult to find simulations for. Sure kids can always use writing to share what they've learned but it is hard to generate hypotheses to learn various writing skills.
    This site has a couple simulations but I didn't try them out: http://www.stagecast.com/cgi-bin/templator.cgi?PAGE=School/LESSONWORLDS

    Doing a quick search revealed that it really is hard to find resources for language arts while focusing o these strategies.

    Is there any way your classes could act out running a newspaper? One person could be the editor, one could be the reporter, and then they could switch jobs at the end of the quarter....

    If I stumble upon any I will definitely send them your way!

    I'd also check out: http://www.interact-simulations.com/c/featuredproduct.html?subject@Writing_2FEnglish+s@AAAHLzXvGfpe2 I've used some of their simulations in social studies and they were great. The copies I have area old and didn't include technology but it was easy to bring in some technology once I read over the books. These aren't free though. :(

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  3. Hi Mindi,

    Thanks for your very thoughtful post. Your project based approach to math instruction sounds very engaging and, as you pointed out, motivating to many students who take it upon themselves to continue on their own time. I'd really like to hear more about some of the projects you do with your fifth grade math students. I also teach fifth grade and our math curriculum consists of five units, three of which we have incorporated project-based learning (number sense, graphing/data analysis & geometry). Do you have any good ideas for a computation unit (very dry), or a unit on fractions?

    Thanks again for your thoughtful post.

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  4. Hi Chad!
    I'm not sure if what I have is exactly PBL but it it somewhat better than drill and kill......
    This is what I've created for one of my checkpoints for Walden so I have not implemented it yet into my classroom. The final activity uses two culminating activities. One requires students to determine amounts of ingredients needed to prepare enough servings, and to determine the amounts left over after making the recipes, the other requires the students to create an artifact to demonstrate their learning. This is very long though so it will make me post it in sections....

    Fraction unit


    Building/Applying Knowledge and Skills by Engaging Students in their Learning

    Day 1: Equivalent Fractions-Modeling with Diagrams
    Introduction-Fraction Video: http://www.youtube.com/watch?v=yR15cCAorQA&feature=related
    This video shows various examples how adults in various professions use fractions.
    Assignment: Students will have one week to interview 3 people to see how they use fractions in their jobs. Students must publish this information on our class wiki page. (They have worked with the class wiki previously with other topics.) Our goal is to have different professions posted for each student and not to have repeated answers. Students will be familiar with this procedure and know that submitting their information early is important so others don’t take their ideas.

    Lesson: Briefly review previously learned fraction skills such as naming fractional parts, adding and subtracting fractions with common denominators, and reducing fractions. Problems will be posted on the SMART Board and students will answer each problem on individual whiteboards and hold the boards up for immediate feedback from the teacher. The class will then review the problems together on the SMART Board.

    After this brief review, the lesson will begin on Equivalent Fractions.
    Video: Equivalent Fractions: http://www.youtube.com/watch?v=mU5249bHGuc
    (This video demonstrates visually how fractions are equivalent.)

    Equivalent Fractions: http://www.youtube.com/watch?v=wL4hICyMLKU&feature=related
    (This video has a cartoon in the middle demonstrating fractions and gold pieces.)
    Pretest: http://numbernut.com/advanced/activities/fraction_quiz_equivlt12.shtml
    Students will write their responses on whiteboards. Or, if time, this will be a center and they can do this independently on netbooks.

    Modeling/Guided Practice: The teacher will conduct a lesson using a SMART Board. She will begin by modeling and thinking aloud the steps needed to make equivalent fractions. Students will have a worksheet with shapes that match the shapes on the SMART Board. Together as a class, they will divide the second shape into fractional parts to make equivalent fractions.

    Day 2: Equivalent Fractions by Multiplying
    The class will do three review problems of dividing shapes to visually represent equivalent fractions on the SMART Board.

    The teacher will then model how to make a larger version of the equivalent fraction by multiplying the numerator by the denominator. The students will practice this skill on individual whiteboards and the teacher will provide immediate feedback.

    Homework: The students will complete an assignment in their class Edmodo space to demonstrate their knowledge of making equivalent fractions by multiplying.

    Day 3: Equivalent Fractions by Dividing
    The class will review approximately three problems on the board from the previous day’s lesson.

    The teacher will then model how to make smaller equivalent fractions by dividing the numerator and denominator by the same number. The lesson will continue with students completing problems that are posted on the SMART Board on their individual whiteboards.

    Assignment: Students will complete a worksheet to demonstrate their ability to make equivalent fractions.

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    Replies
    1. Day 4: Finding the Least Common Denominator

      Review Equivalent Fractions briefly by playing: Melvin’s Make a Match (Matching Equivalent Fractions)
      http://pbskids.org/cyberchase/math-games/melvins-make-match/

      Lesson
      Video: http://www.youtube.com/watch?v=-I37jui1PVQ&feature=related
      Vido: http://www.youtube.com/watch?v=BqVEsG1puVA&feature=related

      Model/Guided Practice: The teacher will present problems on the board. Together as a class they will determine if the smaller number will go into the larger number, if not, they will list the common multiples. As the students say the multiples, the teacher will write them on the board. As they find a common denominator they will shout “STOP!” Together as a class they will identify what was done to each fraction to make an equivalent fraction with the new denominator. They will continue to do practice problems until approximately 10 minutes is left of class.

      Game: http://www.sheppardsoftware.com/mathgames/fractions/LeastCommonDenomimator.htm
      Students will play this game in groups at the SMART Board. Today they will be grouped based on who their teacher was in the 4th grade.

      Day 5: Adding Fractions with unlike denominators.

      Lesson: Review LCD game from the previous day
      http://www.sheppardsoftware.com/mathgames/fractions/LeastCommonDenomimator.htm

      Adding Fractions with Unlike Denominators: The teacher will model how to find LCD, make equivalent fractions and add the fractions. Students will use this site: http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html during the lesson. This site provides fractions and visually represents each fraction. Students can determine the LCD and adjust the images to change the number of pieces it is divided into to determine the new fractions and then add the fractions.

      After 15 minutes students will begin to do problems without the visual diagrams.

      Assignment: Groups will search the web to find age appropriate videos on how to add fractions with uncommon denominators and add at least one video to our class wiki “video lesson” page.

      Day 6:
      Review: The class will review concepts whole-group. The teacher will post problems on the board and students will answer them on their whiteboards.

      Independent Practice: Students will get approximately 20 minutes to play these two games:
      http://www.mathplayground.com/fractions_add.html
      http://www.mrnussbaum.com/ezfractions.htm

      Wiki Assignment (20 minutes in class): Groups will search to find other educational games to practice adding fractions with uncommon denominators. Each group should post 2-3 links on our “Fraction Games” page of the wiki. They should also include a brief description of each game they selected and why it was chosen.

      Homework Assignment (15-20 minutes): Students will solve problems posted in their Edmodo assignment page to practice adding fractions with uncommon denominators.

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    2. Day 7:
      Brief Review of adding fractions with uncommon denominators. Students will answer problems on their whiteboards.
      Lesson: Subtracting Fractions with uncommon denominators (no borrowing)
      Problems are posted on the SMART Board, students answer them on their whiteboards and then review the answers together.

      Homework: Students will answer problems posted in their Edmodo assignment. Problems will be basic subtraction of fractions with uncommon denominators.

      Day 8:
      Lesson Word Problems with adding and subtracting fractions
      http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators-word-problems

      Group Work:
      Each group must create 3 word problems involving the addition and subtraction of fractions. (This is a skill they have practiced earlier in the year.) These must be submitted to the teacher.

      Group Wiki work: Groups must find at least one video on how to subtract fractions with unlike denominators and 2-3 games on this skill and post these to our class wiki. They must include a brief review of the game and a reason why it was selected.

      Homework: Students will need to answer the questions (the word problems created by the class) that will be posted in an Edmodo assignment.


      Day 9+10: Recipe Activity and introduce rubric for final activity
      **This make take a few additional days depending on which hours are assigned the extension component.

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    3. Day 11-15: Final Activity work time in class








      Extension/Enrichment/Transfer or Generalization of Knowledge that Engages Students in their Learning
      This component will have two parts, a recipe activity and a final project in which the students will create an artifact to demonstrate their learning.
      Recipe Activity:
      You and your friends are preparing three deserts for a small party. You must adjust each recipe to serve 24 people.

      As an extension, you are in charge of making a grocery list for the supplies for this celebration. The charity already has purchased some ingredients for the
      celebration. You will be given $75.00 to purchase the ingredients not supplied. To make it easier to purchase these items, a grocery store cost sheet has been
      provided for you. Once again, you will need to consider how much you will need to purchase, based on the serving size of the recipe and people coming to the
      celebration. Don’t spend more than necessary; this is a charity.

      Students will be given copies of the recipes below, worksheets with tables to demonstrate their work, a list of ingredients and amounts of each ingredient they have in the cupboard, and a grocery list of prices for additional ingredients that need to be purchased.

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    4. Chex Mix Puppy Chow
      9 cups Chex
      1 cup chocolate chips
      ½ cup peanut butter
      ¼ cup butter
      ¼ teaspoon vanilla
      1 ½ cup powdered sugar
      Put cereal in large bowl. Melt chocolate chips, peanut butter, and butter. Remove from heat and stir in vanilla. Pour over Chex cereal, put into a large plastic bag with powdered sugar and shake well to coat. Spread mixture evenly on wax paper and allow to cool.
      Yield: 12 servings

      No Bake Peanut Butter Brownies
      4 cups graham cracker crumbs
      1 cup peanuts, chopped
      ½ cup powdered sugar
      ¼ cup peanut butter
      2 cups semisweet chocolate chips
      1 cup evaporated mild
      1 teaspoon vanilla extract

      Combine first 4 ingredients with a pastry blender. In a small saucepan, melt the chocolate chips with milk over low heat, stirring constantly until smooth. Remover from heat; add vanilla. Remove ½ cup and set aside. Pour remaining chocolate mixture over crumb mixture and stir until well blended. Spread evenly in a greased 9-inch square baking pan. Frost with the reserved chocolate mixture. Chill for about 1 hour.

      Yield: 2 dozen

      Fruit Salad
      2 cups watermelon balls
      2 cups strawberries, halved
      2 cups blueberries
      3 medium bananas, sliced
      2 cups sliced peaches
      2 cups sparkling white grape juice
      Combine the watermelon, strawberries, and blueberries in a glass bowl, cover and chill until ready to serve.To serve, add the sliced bananas and peaches; pour the
      white grape juice over the top. Serve with a slotted spoon.

      Yield: 6 servings

      Easy Fruit Punch
      3 cans frozen fruit punch
      9 cans of lemon-lime soda, chilled
      Pour fruit punch into a large container or punch bowl. Slowly add each can of chilled soda. Carefully stir after each addition of soda.

      Yield: 12 servings

      Complete the worksheet to show your calculations on how you adjusted each recipe to serve 24 people. Also, complete the worksheet with the grocery list and calculate how much of each item will be left over after each recipe is made. These worksheets were found online at: http://www.eacs.k12.in.us/site/common/files/ma5bundle3.pdf

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    5. Final Project: Students must pick one of the final projects (or get their project idea approved by the teacher if it is not listed) to demonstrate the skills learned during this class.

      The choices are:
      Create a board game using all the fraction skills that we have learned in this unit.
      Optional: this could be done on the computer using a Jeopardy template, the Survivor Game template, PowerPoint, or SmartNotebook but it can also be done with posterboard or other materials.
      Write and illustrate a storybook. The story must include all of the fraction skills we’ve learned in this unit.
      Optional Online versions: http://makebeliefs.comix.com/comix and http://superherosquad.marvel.com/create_your_own_comic as well as others students find online
      Design a Poster to teach a third or fourth grader everything they will learn about fractions. Include picture examples and write sentences to explain.

      Create a WebQuest or Wiki-be sure to include video lessons, games, and online quizzes

      Write a song, poem, or skit to help learn important fraction skills and vocabulary. Record you performing these.
      Optional: Make a Claymation at ToonBoom Animation or use other software to have illustrations act out or read your text.

      Synthesis/Closure

      This activity will close by taking a day or two to present final projects to the class. I would like to set up centers that will allow students to watch the videos created, participate with the wikis, and play the games the classmates have created.

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    6. Other Favorite Fraction Links (in addition to the ones on my webpage)
      Adding, Subtracting, Multiplying, and Dividing Fractions
      http://www.mrnussbaum.com/ezfractions.htm


      Factmonster.com/math
      Compare Fractions Using Greater Than, Less Than, or Equal To Symbols
      http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw42180

      Find Common Denominators and add Fractions
      http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50630
      *make pizzas (pieces) adding fractions. Need to click on pizza to divide the pieces so they are the same size (common denominator). Discuss what happens to the numerator. Add the fraction. Game doesn’t reduce these.

      Work With Uncommon Denominators (see it visually)
      http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50634
      *Visually represent orders with models
      -1/6 want breadsticks, 2/8 want salads, overlap diagrams, identify fraction that wants both

      Convert Improper Fractions to Mixed Numbers
      http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50629
      *improper fractions
      -cut pizza into pieces, top according.
      -customers eat some of the pizzas
      -type a fraction to show what is left (improper)
      -Convert to a mixed number

      Adding and Subtracting Fractions-May be used with the lesson Find common denominators and add fractions
      http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html
      *fraction is written and modeled. Students can manipulate the number of pieces to change the denominator so pieces are the same size.
      -maybe use after discussing how to use the least common denominator

      Common Denominators (Divide the shape to find a Common Denominator and then place it on a number line)
      http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html

      Melvin’s Make a Match (Matching Equivalent Fractions)
      http://pbskids.org/cyberchase/math-games/melvins-make-match/
      *Great extension activity

      Fun Brain Soccer Shootout (Adding Fractions)
      http://www.funbrain.com/cgi-bin/fract.cgi?A1=s&A2=0&A15=1


      Adding Fractions With the Same Denominator-Practice and 3 Games
      http://www.321know.com/fra410x2.htm

      Adding With Like Denominators (coolmath-lesson and scroll over answers to check your work)
      http://coolmath4kids.com/fractions/fractions-10-adding-with-like-denominators-01.html

      Adding and Subtracting Fractions Board Game
      http://www.math-play.com/adding-and-subtracting-fractions-game.html

      Tony’s Fraction Pizza Shop
      http://www.mrnussbaum.com/tonyfraction.htm
      Mr. Nussbaum’s online worksheets
      http://www.mrnussbaum.com/fractions.htm

      Quiz
      http://www.thatquiz.org/tq-e/math/fractions/reduce/

      (Reducing Fractions, Adding) Select Number of Problems and Difficulty
      http://www.thatquiz.org/tq-e/math/fractions/reduce/

      Reduce to Simplest Form
      http://www.ixl.com/math/grade-5/reduce-fractions-to-simplest-form

      Least Common Denominator
      http://www.ixl.com/math/grade-5/least-common-denominator

      Add and Subtract Fractions with Like Denominators
      http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators

      Equivalent Fractions
      http://www.ixl.com/math/grade-5/equivalent-fractions

      Add and Subtract Fraction Word Problem
      http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like-denominators-word-problems

      NUMEROUS LINKS for Fraction Quizzes
      http://www.ixl.com/math/grade-5

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  5. We also LOVE singing our fraction songs....they get annoying but they work! I put them in my SmartBoard files and we sing them every few slides. We also have some actions for parts of the songs. I'll try to post these to my main page. :)

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