Who thought this would best suite the educational field?
With regards to the traditional way of teaching and constructivist teaching is there anymore evidence that there is no difference?
What are some other proposed strategies that have not been implemented into the classroom, but are being worked on and looked at now?
How long does it take for ideas such as constructivism to be implemented into the educational system?
What are some constructivist ways to assess students in the classroom, beside the traditional methods?
Should the teacher always act as a facilitator, or is there any evidence that the teacher should be actively involved by other means within the classroom?
What are children's views on constructivism? Do they enjoy it?
Will constructivism work in classes of really large or really small numbers of students?
How does culture play into the success of establishing a constructivist classroom?
Does constructivism in the primary and elementary grades lead to higher academic achievement in middle and high-school?
Monday, March 19, 2007
A Final Thought...
Trying to cover the topic of Constructivism in Mathematics Classrooms was quite an undertaking. The amount of activities available for teachers to use in their classroom is endless. As you might have noticed, we only included a small sample in our blog, and instead focused on the foundations and conditions needed to establish and maintain constructivism principles in the classroom. However, we have not left you high and dry! On the left hand side of this blog are websites that provide countless activities for any grade level. After much internet surfing we have selected these and stand behind them.
We hope you have enjoyed our blog and that you leave ready to bring constructivism to your current, or future classroom!
Thank you,
Tara Tobin & Amanda-Rae Warren
We hope you have enjoyed our blog and that you leave ready to bring constructivism to your current, or future classroom!
Thank you,
Tara Tobin & Amanda-Rae Warren
Ideas for the Classroom
Some Ideas for classroom teachers to keep in mind:- Teachers could use is arranging the classroom so that students can and feel free to work with other studentswhen having difficulty or trying to complete a task. Sometimes that is one of the most beneficial things a teacher can do to help his or her students.
- The comfort level that exists in the class is key for students taking risks, if students feel that they can express themselves then they will enjoy risk taking and exploring different methods of trying mathematical problems.
- Another thing that teachers can do is to have a variety of materials available for students to experiment with and work with. This opens students minds to a variety of possibilities.
- Allow for games and activities to be placed around the classroom at all times so students can work with them on their own time, as well ensure that these activities incorporate a variety of learning styles, such as kinesthetic, visual, and auditory.
- One key point that should be encouraged, is making sure that students questions are answered. Because students are curious and need help in understanding certain ideas, concepts, or just want to make sense of things. This can be done to help students. For example if students are having trouble with integers, then relate them to the weather (Class notes, mathematics winter 2007). There are a wide variety of ways to do this, this is only one example.
Possible Activities for Primary and Elementary Students
As Clements (1997) maintained, constructivism is more than just teaching, it's a philosophy of learning. Here are some activities that are excellent examples to use for a unit on geometry, area, shape or space in a constructivist classroom:- Triangle areas
- Shape-construction game
- Magic Bugs and Mobius Strips (strategy/problem solving)
- 3-D tic-tac-toe (spatial skills and strategy/problem solving)
- 3-D Shapes
- Geometric Shapes Colouring
- Tessellations (Mobius Strip)
- Polygon and tower construction with wooden pieces (stimulating geometry discussion)
Can we do it? Yes we can!
So, now that you have the literature, you have the background and you know the facts - can you bring it?? That is, can you bring constructivism to your classroom? We know, it's nerve wrecking. But no one said it would be easy right? As we figure it, there are basically two ways to start thinking constructivily. You could:
A) Dive right in with the information you have and see what happens, or
B) Start gradually, and immerse yourself and your students into the world of constructivism slowly.
Althought both options have their merits, our research leads us to conclude that option B is probably the better route. We've come to this conlcusion for different reasons.
A) Dive right in with the information you have and see what happens, or
B) Start gradually, and immerse yourself and your students into the world of constructivism slowly.
Althought both options have their merits, our research leads us to conclude that option B is probably the better route. We've come to this conlcusion for different reasons.
- better equips new-constructivist teachers to maintain classroom management
- teachers can optimize success for themselves and their students when they start with a few good lessons compared to many poor ones.
- teachers can observe students reactions to this "new" type of learning and change their instruction accordingly
- Starting slowly can also mean teachers have a chance to build up resources
Constructivism in Action!
What might constructivism look like in a real classroom? Check out this video of a "Math Night" at West Mercer Elementary School in Mercer Island, Washington. Notice how the children are engaged and seemingly enjoying participating in, and demonstrating to their parents, various math activities. What a great idea!
Constructivism and Teaching Mathematics in the Classroom
There is much debate today as to when constructivism first began, what exactly is included in a constructivist classroom and how to run these classes smoothly. In a constructivist classroom there needs to be an open environment, one in which children feel free to express themselves in new and creative ways. This is important and one of the main reasons why play and experimentation is so important. We all learn through our environments; therefore, what better way to learn than through direct interaction with the environment.
The same goes for the math classroom. Exposing children to manipulatives and other items which will help them during math class (although sometimes frowned upon) is an excellent, and pretty standard, constructivist practice - but there has to be a distinction as to why one is using or doing so. In the article “Middle School Mathematics Reform: Form Versus Spirit,” Gary Tsuruda (1990) states that in the traditional way of teaching, students that are exposed to manipulatives only once or so and this is not enough to help students. Manipulatives can be used to help with almost every topic in mathematics, but their effectivness will be determined by the way in which the teacher incorporates them into his or her lesson.
Although on the otherhand, one might ask is constructivism really as beneficial as some people think? According to one study done by Insook Chung at Saint Mary's College, Notre Dame, Indiana, the difference between two schools of instruction and learning (constructivist vs. Traditonalist) was non-existant. In fact, it showed that students really had little difference while being taught multiplication in a traditional or constructivist method. For us, this raised the question of does constructivism really make a difference or was the constructivist classroom created properly? As, Gary Tsuruda states, a classroom can have the look of a constructivist classroom, but does not have to run like so. For example, the desk can be put into groups our, yet no students have to work together ( Tsuruda, Pg. 6). Clements (1997) raises similar issues when he discusses the teachers who practice "constructivism on fridays."
The fact of the matter is that constructivism is a philosophy, a practice and an atmosphere. Students have to be shown that they are permitted to help each other and are able to work together to solve problems ( Tsuruda, Pg. 6). In our experience through our observation days, we have come into contact with all kinds of new and motivating ways to promote independent learning for students. One example that comes to mind is allowing students the opportunity to express their answers in different ways and not be condemned for doing so. This is constructivist learning at its finest. Pentominoes are a great way for children to discover new ways to express their answers. This involved students creating different shapes out of blocks, which taught the concepts of shapes and patterns, while not restricting children to simply read a text book.
There is more support for constructivist learning now, more than ever before. This is especially true since there has been more studies done in the past decade that study and promote the effects and benefits it has for students and all learners. One thing that comes to mind is Gardner’s Theory of Multiple Intelligences. This has had a big impact on the way some people teach there class. This concept also ties in with the idea of constructing knowledge. Because if students are permitted to complete tasks in ways that help them learn and process information more efficiently then are we not doing our job as teachers? This is the challenge, but as educators we must try and overcome to the best of our abilities.
The same goes for the math classroom. Exposing children to manipulatives and other items which will help them during math class (although sometimes frowned upon) is an excellent, and pretty standard, constructivist practice - but there has to be a distinction as to why one is using or doing so. In the article “Middle School Mathematics Reform: Form Versus Spirit,” Gary Tsuruda (1990) states that in the traditional way of teaching, students that are exposed to manipulatives only once or so and this is not enough to help students. Manipulatives can be used to help with almost every topic in mathematics, but their effectivness will be determined by the way in which the teacher incorporates them into his or her lesson.
Although on the otherhand, one might ask is constructivism really as beneficial as some people think? According to one study done by Insook Chung at Saint Mary's College, Notre Dame, Indiana, the difference between two schools of instruction and learning (constructivist vs. Traditonalist) was non-existant. In fact, it showed that students really had little difference while being taught multiplication in a traditional or constructivist method. For us, this raised the question of does constructivism really make a difference or was the constructivist classroom created properly? As, Gary Tsuruda states, a classroom can have the look of a constructivist classroom, but does not have to run like so. For example, the desk can be put into groups our, yet no students have to work together ( Tsuruda, Pg. 6). Clements (1997) raises similar issues when he discusses the teachers who practice "constructivism on fridays."
The fact of the matter is that constructivism is a philosophy, a practice and an atmosphere. Students have to be shown that they are permitted to help each other and are able to work together to solve problems ( Tsuruda, Pg. 6). In our experience through our observation days, we have come into contact with all kinds of new and motivating ways to promote independent learning for students. One example that comes to mind is allowing students the opportunity to express their answers in different ways and not be condemned for doing so. This is constructivist learning at its finest. Pentominoes are a great way for children to discover new ways to express their answers. This involved students creating different shapes out of blocks, which taught the concepts of shapes and patterns, while not restricting children to simply read a text book.
There is more support for constructivist learning now, more than ever before. This is especially true since there has been more studies done in the past decade that study and promote the effects and benefits it has for students and all learners. One thing that comes to mind is Gardner’s Theory of Multiple Intelligences. This has had a big impact on the way some people teach there class. This concept also ties in with the idea of constructing knowledge. Because if students are permitted to complete tasks in ways that help them learn and process information more efficiently then are we not doing our job as teachers? This is the challenge, but as educators we must try and overcome to the best of our abilities.
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