Encouraging Hands-On Learning
One of the big takeaways from this week was the importance of incorporating hands-on learning in math class, especially for geometry. In Chapter 17 of Making Math Meaningful, Marian Small discusses the Van Hiele Taxonomy of Geometric Thought which contends that a child's spatial experience is critical in developing their geometric thinking. In order for students to develop spatial abilities and a strong understanding of shapes and their properties, they need opportunities to physically interact with shapes. I can certainly relate to this research. When I can touch the shape's faces, edges, or vertices or rotate the shape in my hands to see it from different angles, I have a much better understanding of the shape's properties.
One way to provide students with these important spatial experiences is through the use of tangram squares. Students can combine different tangram squares to create a variety of shapes such as triangles, squares, trapezoids, parallelograms, and pentagons. This activity of dissecting and combing shapes can help students to gain a better understanding of the properties of shapes. For example, students might discover that a parallelogram can dissect into two congruent triangles. This might be helpful in the future when they need to calculate the area of a parallelogram.
 |
| Olij, B. © 2016 |
During the learning activity presentation, Lianne introduced another way to interact with shapes. This time, we created 3-D shapes by using jujubes and toothpicks. This hands-on activity is particularly helpful for students to gain a better understanding of what a shape's edges (the toothpicks) and vertexes are (the jujubes).
 |
| Olij, B. © 2016 |
Another example of how to provide students with spatial experiences came from Marian Small's Making Math Meaningful. Small suggests using pattern blocks to allow students to sort shapes based on their common properties. This can help students to understand how the different shapes are related to one another.
 |
| Retrieved from Making Math Meaningful to Canadian Students, K-8: Third Edition, p. 399. |
Asking Effective Questions
This week I was also reminded of the importance of asking my students questions. I had an "ah-ha" moment during class when Pat discussed how asking students questions is a way of showing our students that we have faith in them. I had never thought about the importance of questioning in that way before, but it is so true! Students feel confident and empowered when they take responsibility for their learning. I found the Capability Building Series document entitled "Asking Effective Questions" to be very insightful. As the document discusses, asking questions encourages students to actively create their knowledge as they build new understandings and connections. Not only do teachers need to ask questions, but they need to ask effective questions that promote inquiry and thinking.
While all eight of the tips that the document offered for asking effective questions were insightful, there were three tips that really stood out to me. The first is to "pose questions that actually need to be answered." While this may seems obvious, I know that I can fall into the habit of asking students rhetorical questions. This is not very helpful as it simply provides students with the answer and doesn't allow them to engage in their own reasoning. Another helpful tip is to "keep questions neutral" by avoiding qualifiers such as easy or hard as this can intimidate or discourage students. As a teacher, I need to choose my words carefully. The last tip that really stood out to me is to "provide wait time." When time is short and it feels like there is a lot to get done, it can be easy to rush the students. By allowing a wait of even just three seconds, this will likely result in a better quality and quantity of responses. Many students need time to digest information and to formulate their thoughts or words; it is important that I give them time to clarify and articulate their thinking.
Hi Belinda, I really enjoyed reading your post this week! I think that one of the biggest things that I took away from the class this week (and most other classes for that matter) was the use of manipulatives. Tangrams are a great way to get students thinking and creating when it comes to geometry and spacial sense. Additionally, tangrams allow students to start and create whatever they want. Everyone's shape might look different, no matter what instruction you give them. It's a great way to spark creativity and let students mold their own learning experience! I know that I definitely appreciate hands-on activities in math, so I can only assume that other students (no matter what ages) would also appreciate them. Manipulatives are a vital part of learning math!
ReplyDeleteHey Belinda, your post this week was fantastic! I also agree that one of the biggest takeaways that we should have from this class and most of the classes is that students should be offered physical opportunities to explore in mathematics. The chance to explore with the use of manipulatives will allow students to better understand the different aspects that are associated with that specif task. The two ways that you provide, use of tangrams, and creating 3D objects are both extraordinary resources that can be used. Your take on effective questions is also very well done. The three tips that you chose can really have an effect on students. I think as teachers we tend to label questions as easy and hard and as you stated it can deter students from trying to find an answer. As teachers we should continuously refer to these tips to help ensure our students are able to have the best learning experience possible.
ReplyDeleteBelinda, your post was really great to read! I liked the fact that you focused on the importance of hands-on learning because it really does make a difference! Having the opportunity to use manipulative's especially in topics such as geometry where the unit it all about shapes, is crucial to have all students understand and grasp the main idea of the properties shapes have. Also, the point you made about the spatial experience was perfect because without having that knowledge to touch and play around with shapes you won't effectively gain the knowledge to physical see the properties. In response to the section of your blog about the effectiveness of questions, I couldn't agree with you more on the last tip about giving students time to answer the question at hand. Too many times have I seen students feel like they need to answer something fast because if they don't it seems like they don't understand. But that is not the case and you have reflected on that point wonderfully.
ReplyDeleteHi Belinda,
ReplyDeleteI have to agree that the most important thing with learning about geometry is allowing students to be hands-on. I love the variety of photos and examples you provided that we were able to use in our class last week. I find that often is forgotten that there are so many different ways to incorporate student-centered learning and allow them to challenge themselves in the process. And with that in mind, it's important for us to remember that it takes time for students to process and critically think about the questions. By doing so it will allow them to show their true learning potential and allow us as teachers to effectively assess their work.