Transitioning requires a great deal of planning. It’s a trial and error. If things work out, then continue doing it and try to improve it. If not, devise some ways wherein kids could be able to get it. Anything new for students will be difficult because we are trying to get them away from their comfort zone. As I have said, it requires lots of planning. We need to motivate them. Programming could help a lot in transitioning if we could be able to relate the importance of it in algebra and be able to make connection in a real world situation
Giving students visual representations of real life situations always works for my students. I believe that programming will help students transition from concrete to abstract concepts as this will give them an opportunity to apply math in real life.
I like your example giving students an equation and then for them to come up with the context, t-table and graph. Will try next school year! Thanks for sharing.
I am not sure I have found anything that truly works to help all children transition to algebra. Technology, when it is applicable, helps some students but not all. Technology done right can definitely bridge the gap for some students; however, I have not found any truly integrated technology (only games and tutorial activities). I believe CODE truly embodies algebra, and if we can get students to have enough patience to work towards the end results (or allow them to incrementally see results), theywill be motivated to learn. Then it will simply be up to the teacher to show the connection between the the coding and the Algebra.
I believe that abstract thinking comes at different times for each student. There is a maturity that must take place before students can make that leap. Manipulatives such as algebra tiles help a lot for students who struggle with it. Technology and visuals are important to help students in that direction.
I do agree that finding the connection is the key. And knowing how to use that connection to teach abstract concepts is what we all looking for. However, I think that visual technology by itself is a tool to get students attention and let them engage with difficult concepts in Math. If we can show them the connection between algebra and computer science. I guarantee you they will be more excited to learn.
Many of my students have a hard time thinking about abstract concepts. They usually gain some understanding if I can come up with a real world problem that they can relate to. I think programming can help get the students interested in algebra. If they don’t write the correct function then the program does not run correctly. Then, they have to find their mistake and correct it.
I like the idea of breaking large problems into parts. I do this with my students as well. I also have a hard time getting them to see the whole picture when they are finished.
I agree that maturity play an important role in students grasping abstract thinking. Many students need a visual to help them understand.
I have found that i have the most success when I can use something concrete, like Algebra tiles, and then model the same problem in algebra so they can see how the two connect. I have always found that I can model every concept concretely, though. Also, i find that if I simplify a problem to show them the “why” something works and then move that same process into a more difficult problem they can grasp it easier. For instance, when my algebra students are faced with making a common denominator in an algebraic fraction, I first revert back to basic fractions and we discuss the how and the why of getting common denominators and then we move back to the more difficult problem so that they connect that the process is the same. The most difficult part about all of this is time. Some of my students can see it once and get it. Others need to see it 20 times and balancing the time it takes to help those students while not holding back my quicker students is a huge challenge!
Many times as I’m teaching math students want to argue whether something has relevance to their lives or not. I think that this will be a great way for them to have a hands on experience with something that gives relevance from the math we are learning in class to the real world and something that interest them.
I think that seeing the reverse of how the games/apps work will open my student’s minds to be able to grasp different concepts by not taking the “head on”
Using games has worked for me well in the past. I’m excited to use computer gaming as a vehicle to teach more math concepts.
Our math team does our best to create a many opportunities as possible for students to connect the abstract concepts to real world practical use.
I haven’t done a lot of programming, but what we did do was challenging for students and it was great watching them collaborate and problem solve and seek out the answer instead of only depending on me.
I use a lot of algorithms to solve basic understandings of algebra, in which students can use these algorithms and apply them to newer concepts. Algorithms break down algebraic problems into smaller pieces and they can create action plans to help them solve the problems. Also, making connections to previous concepts can help them understand it better.
I have not taught Algebra as a full course, but I have introduced it to my 5th graders. I can tell that sometimes they struggled with a variable being a letter and how to find the opposite math operation to just solve for x.
My general approach w/ Algebra as I introduce to my students is that we are going to find Patterns. As human beings we are natural Pattern Finding Machines and that Algebra is a method used to help describe and or analyze the pattern we see. Patterns begin as numerical and then slightly more abstract with the use of variables. We also look at picture patterns and related them to what we know numerically.
Students find it difficult to transition between the numerical to the variable representation of a pattern. The notion that something works based on a series of numbers you are familiar w/ is much more difficult when you suggest that this Pattern continues for ever and that this “Generalized” version includes a variable.
The use of Programming will probably help me bridge this gap a bit better given that programming is Goal oriented. The program may not even include numerical values, but rather a set of instructions all of which need to work together in order for the task to be achieved.
I have my student create a table and they have to catch problems that are in equation, word, table, or graph forms.
I have typically tried to connect it to previous knowledge. Show them the concrete model and then show them how it applies to the abstract. I have also found showing the students multiple representations allows them to have a favorite representation that maybe they understand most and then they can connect that favorite representation to others they don’t understand as well.
I think it always helps students to understand abstract concepts if they are introduced in context so that students can relate to. Students are much more willing to learn if the math they are learning has some meanings to them; something that they can relate to in real life. I think computer science in the forms of game, animation is a great way to hook students into learning the underlining mathematical concepts