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
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!
ReplyDeleteMary
ReplyDeleteI 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. :(
Hi Mindi,
ReplyDeleteThanks 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.
Hi Chad!
ReplyDeleteI'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.
Day 4: Finding the Least Common Denominator
DeleteReview 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.
Day 7:
DeleteBrief 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.
Day 11-15: Final Activity work time in class
DeleteExtension/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.
Chex Mix Puppy Chow
Delete9 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
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.
DeleteThe 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.
Other Favorite Fraction Links (in addition to the ones on my webpage)
DeleteAdding, 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
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. :)
ReplyDelete