▪ How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities? Provide examples to illustrate your points.
Throughout this course, we have been discussing how students construct knowledge and understanding. In short, I think we can all agree that the most practical way to teach students is to give them multiple opportunities to explore and collaborate while scaffolding their learning and providing different means for them to express and apply their understanding. Traditional methods of memorization are no longer viewed as best teaching practices. Instead, we want students to build knowledge through concepts so they can apply what they have learned in problem-solving contexts. In Erlwanger’s (1973) article he reminds us of the danger of teaching mathematics without ensuring that students have a proper conceptual understanding and that memorizing procedures through rote learning can be ineffective. I can definitely relate to this article as I have seen many examples of when students have memorized how to complete a set of questions but cannot apply what they know in a real life application or when they are given an open-ended problem. Many of my students go to Kumon so they can complete a long series of questions quickly but many have no idea what they are doing. They have simply memorized an algorithm. For instance, I have a student who can complete 20 2-digit by 2-digit multiplication questions in under 3 minutes. But when asked to complete 22 x 4 in his head he cannot. Other students in my class who have no idea what the traditional algorithm for multiplication is, let alone how to use it, could answer this question because they understand what multiplication is. They know that it is adding equal groups and can partition the numbers using mental math and will add 20 groups of 2 to 2 groups of 2.
It was very interesting to read about how to use informal spaces to construct knowledge and build conceptual understanding. The topic of field trips is something we are continually talking about at school because we want them to enhance learning and help construct conceptual knowledge, but more often then not, they become stand-alone lessons where the students are learning in isolation information that isn’t necessarily connected to the goals we want to achieve. Yoon et. Al (2012) examines the potential that these informal spaces can have to increase students conceptual understandings of science. They found that using augmented realities to replace tradition text guides would keep visitors more engaged and therefore “improve access to information and increase exhibit functionality.” (Yoon et al. 2011). After browsing the Exploratorium Museum’s website that is located in San Francisco, you can see that they have created many galleries and exhibits that would let visits explore concepts using elements of embodies learning. Instead of just viewing and listening to information, visitors have the opportunity to test and create and explore different ideas. This is very similar to the pedagogical model that we want to see in schools.
I think that using informal spaces and going on field trips can be influential in building conceptual understandings. When planned and executed in a meaningful way, it can give students opportunities to apply what they have learned in class in the real world as well as see ideas and gain new perspectives. Just like we have seen with materials like Jaspers, teachers don’t always need to be the ones who are delivering content. Using spaces like museums is another tool that we can utilize to help students inquire into the world around them and construct their own knowledge.
References:
Erlwanger, S. H. (1973). Benny’s conception of rules and answers in IPI mathematics. Journal of Children’s Mathematical Behavior, 1(2), 7-26.
Yoon, S. A., Elinich, K., Wang, J., Steinmeier, C., & Tucker, S. (2012). Using augmented reality and knowledge-building scaffolds to improve learning in a science museum. International Journal of Computer-Supported Collaborative Learning, 7(4), 519-541.
Sarah,
I love the idea of using AR to supplement trips to a museum. Imagine how this could enhance the experience when put together with the idea of something like Google Glass. With one tap, students could look at an exhibit with their own eyes, with another, an interactive annotated version (think, a stepped-up museum sign) could show the inner workings of what is going on, diagrams of design, or even make it interactive by asking questions or quizzing them on what they have already learned. All of a sudden, the exhibit would be interactive and engaging for every student, as their learning would be personalized to what they are interested in. I could see this as a beautiful addition to any museum.
Furthermore, those same simulations could be available virtually to people who can’t physically go. This would enhance the accessibility and help bridge the gap that exists in many less privileged places.
It would be even better if those same AR simulations were tailored for each student based on what they like to look at in their free time. Wow, the future seems like an amazing time!
-Jonathan-
The possibilities are endless! I love bringing my students to museums but in big groups, it can be a challenge to keep them all engaged, listening and on task. With ideas like these where students can move through more at their own pace and have a bit of ownership over their inquiry, I think would be a more meaningful experience!
Thanks!
Sarah
Dear Sarah,
I appreciate your thoughts about utilising the virtual space for educational purposes. Museum visits should not be stand alone lessons. There are many promising application already available at major museums. For example, Story of the Forest in Singapore (http://nationalmuseum.sg/our-exhibitions/exhibition-list/story-of-the-forest?sc_lang=e) or digital English cities (http://www.heritagecities.com/stories/explore). We live in an exciting age!
I think you allude to the idea that math should be understanding via problem based learning. i am curious to hear your thoughts about how educators can better support students as they practice identifying concepts in problems or project based learning.
Thank you for your thoughts.
Sincerely,
Alice
Hi Alice,
I agree, there are some great informal spaces where we can bring students, but depending on where you are in the world it can be a struggle to find meaningful connections. For instance, when I was in Beijing, they had a vast amount of interactive spaces, but many of them had no English so were not accessible to most of our students. I love the idea of a virtual field trip to overcome this language barrier, but again it won’t work on all instances.
I think that Math should be taught with an open-ended inquiry-based approach, where students are given problems to solve where they need to apply what they already know to both reinforce their knowledge and to build new understandings. One resource I use often is Peter Sullivan’s book ‘Open-Ended Math Activities’ where he has created a large number of problem-solving questions for different Math strands at different levels. These questions are created to encourage students to use the knowledge they already know and push their thinking as there is always more than one correct answer. Once they have established a strong conceptual understanding of the concept you want them to know, is when I would introduce a summative task where students have the opportunity to apply what they know in a real-life context.
What are your thoughts on project-based learning?
Cheers,
Sarah
Hi Sarah,
I enjoyed reading your post and I agree strongly when you state that “I have seen many examples of when students have memorized how to complete a set of questions but cannot apply what they know in a real- life application or when they are given an open-ended problem. I have observed the same thing in my teaching which is why it’s important that educators use real-world problems and applications so that students can apply what they have learned otherwise they cannot relate to it and try to find ways to memorize how to do certain math problems. I like the idea of using augmented realities to enhance learning and participation. Like you said, “when planned and executed in a meaningful way…” I know that I have stated this many times throughout this course but there has to be meaning and intent behind everything that we do in our teaching.