I try to give my students several different ways of why something works. Having them be able to have a visual model to refer back to and then the computation that goes with it seems to be a big help. And of course if they can see how it relates to them they have a buy in for really trying to connect with things and understand them
With my sixth graders, I use Hands on Equations to begin solving equations. We start with the manipulatives, move to drawings, and then on to solving equations. Some students always need the manipulatives, others are ready to start at the equation stage. Connected Mathematics also has a some great lessons using coins and pouches that is really great at providing context to solving for a variable.
I am unsure at this point how programming can help with the transition, but I am excited to learn more about this!
Some of my most “resistent” math students hate the idea of math and all it entails, but love technology and have expressed an interest in coding. I always think of one in particular who seemed to hate all things related to school but would sound so passionate about tech whenever he had a chance to talk about it. If I can learn additional ways to introduce the connection in class, I hope to “hook” all my students.
I try to talk to my students about the math and relate concepts to real life applications. If they understand the everyday concept, they are generally more open to trying the abstract on paper.
I hope that programming will provide a real and valid everyday application for my students to connect with.
My students often have difficulty with graphing and slope. To help with this, we have used the tiles on the floor and the students to plot the points, determine the slope, and find points of intersection. This concrete method makes the abstract of using the graphs to answer word problems easier. I think that computer programming will give them a greater understanding of the abstract and the concrete.
My students have difficulty with mathematical vocabulary in word problems. To help with his problem, I tend to draw a diagram to visually represent quantitative information in a given word problem. The model method offers a powerful and potential tool for children to bridge the gap between arithmetic and algebraic thinking and is believed to have enabled children to solve mathematically challenging problems. Programming can help with the transition by producing the visual.
I believe that you have to tie the math to something that is familiar and relevant to the students They often ask when will we ever use this in real life? I know some students need models and manipulivites to develop the understanding. I use Hands On Equations kits when my students are first learning to solve equations. I am curious to see how programing will help,
I am looking forward to learning along with my students. I am excited and hope relating Algebra to Programming will be fun and exciting for the students.
I do very little to help students transition for concrete arithmetic to abstract algebra. With the direct connection of Math to Coding, I am hoping to find different insight to how I am already teaching.
I am hoping that working directly with the Algebra teacher, we will help students with their understanding of Algebra concepts.
I have used scenarios with money, algebra tiles and other manipulatives to help students transition from concrete to abstract.
Programming will help students develop their thinking skills and to check their work. It will also help them see the relevance of math in the real world. Students find it difficult to understand that variables are not just letters, but that they correspond to numerical values.
We used Code.org extensively in our CS class. One thing that we’ve been thinking about is whether or not to introduce the math before or after the activity. For the lower grades, say K-3, we just let them go at it and let them make the connections later. But with the upper grades do we introduce an activity, such as Graph Paper Programming, with a discussion of functions first? I personally like to let them use programming exercises to come to understanding of ideas and then make the connections. If we start out with the math, many kids will shut down and see the activity as a trap.
The hardest thing for my students is finding the connection, “How does this really apply to me?” If I can find a connection between anything they love and math or even programming then I can help them make the transition from arithmetic to algebra.
In the past, moving from concrete to abstract requires that critical middle step of representation or iconic models. However, there is also a great deal of time required in order to allow students to move through the models and into abstraction. In an earlier post, I said that my students’ experiences are largely about answer-getting, and a lot of Algebra is not that, but instead is about recognizing relationships.
I have almost no experience with programming and cannot say how it will benefit my students in transitioning from concrete to abstract. However, if the coding work a student does can be tested (and by tested I mean the program either runs or doesn’t) and students get immediate feedback (either it works or doesn’t) on their work, then that to me seems like a huge benefit.
To help students transition from concrete to abstract, the problem must be clear and they must know the process of solving the problem. The students must know how to represent the variables in the problem, representations must be concrete and they must be able to establish connections. Students find it easier to understand if the problem has connection with real life situations/experiences. If the problems is so abstract to them they find it difficult to make representation /or establish connection. My students find it difficult to translate a challenge into mathematical expression causing them not to solve the problem correctly. Modeling and chunking the process and teaching them how to make representation made the process easier. I believe that using the right programming will help my students understand the lesson. Through correct programming students will be able to make correct representation, which will help them make abstract information concrete so they can make the right connections.
I hopeful that coding in algebra will help my students build perseverance. I’m also hopeful that it will provide an opportunity for meaningful practice in the short time I have with my students.
Something I have done with my students when dealing with multiplying by fractions is to go back to a bar model. When drawing a bar broken up into thirds and saying the entire bar is equal to 9, students are able to figure out how much each third then needs to be, then they can find any combination of a 1/3. I use this to help students when using the distributive property of fractions into whole numbers, 2/3(9x+6). Then to press students conceptually, I give them a decimal they should be able to change into a fraction and have then distribute again checking to see if they understand the visual model and then eventually, move away from it.
I think that exploring computer language and programming will enhance students mathematical knowledge and help them understand the application of mathematics to real life events, as well as in computer science. A lot of my students want to be “gamers” when they grow up, however they often are unable to see the connection between Algebra, computer science, and real world. Therefore, I think that integrating code in any math class will not only engage students in their own learning, but excite them about math and help them realize that with mathematics and computer science the possibilities of exploration and invention are endless.
I agree completely. I also hope that it will help engrain the process while programming.