Think about the tricks and techniques that you use to help students transition from concrete arithmetic to abstract algebra. Post some thoughts to the forum, considering:
The students need to make a connection and if we introduce technology it needs to function well and be user friendly.
I think programming will help my students. I have taught 8th graders programming this year to build video games. It “forces” them to check their work. If the program does not work, they are “forced” to go back and find the error. They are motivated to this because they really want their program to work. They become much more aware as they are writing their code because they don’t want to go back. It is so cool because they get quick feed back, can fix their mistakes, and they feel great when their program runs. It also helps them to work through frustrations and not give up.
I think that students need to think abstractly about Algebra. They need to be able to apply Algebra concepts when developing skills for jobs of the future.
I find that anytime I relate concepts to my students everyday life even if it’s just bring up a music artist they know, they are more willing learn the concept I am about to teach. Having students experience something new or related to their own life helps them transition.
My students have great difficulty explain their thinking. They are often able to understand a concept, but they can’t fully explain why and how they got their answer.
I hope computer science will bring my students another outlet of learning material. I also hope it will allow them to see a different way of understanding the material so that they can better explain their own thinking afterwards.
Since this will be the first year I will be teaching Algebra at 6th grade I don’t know of the difficulties but I can for see some in the future. I know for me Calculus was so difficult because it was learning in the abstract and I HATED it. I can see where kids who are use to times tables or simple equations can few this as a foreign language. So by using code we can take the abstract ideas out and place more concrete and inventive ideas in front of them.
Technology needs to be updated and user friendly in order for the programming to work effectively in the classroom.
I taught 6th grade Level 1 and Level 2 students this year.
We started with Solo cups and patterns with symbols.
Then we went on to Frozen on Code.org
Some hated it, bored out of their minds. While others loved it and wanted to do more and more. They wanted to progress faster than I could teach it!
I have had students draw and label diagrams. Students sometimes have difficulty that when problems involve unknown values that are equivalent, they often want to write two different variables for each quantity. I am not sure at this point how programming will help.
I have students go back and forth between breaking the problem into smaller chunks and doing it as a whole. When the problem is very complex as whole, I know that they can do the parts. Sometimes, however, they get good at the parts and have to learn to see the problem as a whole again.
I agree with others that making a connection seems to help the students to transition to the more abstract thinking. When my students did do a little bit of coding they found it difficult when the the math didn’t match the demands in the computer programming. However when the math match the coding language I saw it all click for the students.
I’ve found that connecting what we’re doing in math to their lives or giving more hands on approach at the beginning allows them to make connections in the beginning. What my students have difficulty with is then applying this knowledge in a different context or situation. I’m hoping computer science will help them bridge that gap and increase their critical thinking skills when solving problems.
I think students are all different. Many students need to go through a process:
concrete (manipulatives) to semi-concrete (drawings) to semi-abstract (equations with the drawings) to abstract (equations).
I have used algebra tiles over the past few years to introduce different algebraic concepts and have found that some students really need to manipulatives to understand. These students ask if they can use the manipulatives on quizzes and tests, etc. At that point I explain how they can draw pictures to represent the manipulatives and could do that any time. There are other students who have a difficult time. Using the manipulatives seems cumbersome. When they see the process they are like “So, that’s all you have to do”. They immediately see the math procedure whereas are confused by the manipulatives.
What has worked is relating real-world situations to equations and manipulatives. Students find translating word problems into equations most difficult. I think programming will give them an opportunity to use algebra in a way that will be a visual/spatial representation of the problem.
I think students need to make algebra applicable to their lives to make it relevant for learning. My students constantly ask me when they are going to use a specific concept in real life. Sometimes I struggle to answer them because I’m not exactly sure when it will. I think programming will give students a real world application to hold on to and make the learning of algebra more important.
I teach gifted accelerated students and they usually do not like manipulative. They feel it is a waste of their time and want to get to the actual problems. I still have those few who need the concrete application before they are ready to move on to the semi-concrete and then on to the abstract. That is when differentiation is so important; if a student is able to conceptualize a concept without the manipulative and is ready to move on to the abstract they should be allowed to move on while those who still need that hands on approach are able to use the manipulative as long as they need it.
I use manipulatives, real life examples, and visuals any time that I can. I want the students to understand the concept not just memorize how to solve a problem. They need to have as much of a foundation as they can to build on for future math classes. My hope is that the programming will give them deeper understanding and allow them to see some real life applications of math.
What has worked for me is to use real-world examples and models to transition from concrete arithmetic to abstract algebra. I then have the students use these same things in a mini task to formatively assess what they’ve learned.
An example of this is when I’m teaching functions, I give the students an equation and have them come up with a context, t-table, graph, and block model to illustrate the function. Their favorite part is coming up with the real-world context (school appropriate, of course), and they present it in a poster to the class.
Programming could help by providing feedback (just as creating the poster in my mini-project) to the student to check for and to ensure understanding. The student could also have some choice (like creating their own context for the function), which would help create buy-in and encourage perseverance.
As a former algebra teacher I have used algebra tiles for students who are more tactile learners. This method strengthened their conceptual understanding of integers, equations, and even polynomials. However, it was usually those students who struggled with problem solving and or the application of algebraic methods to real world experiences.
As a computer science teacher and having the background knowledge of the algebraic content, I can see how programming can help students with algebraic concepts. For example, when working in the Scratch program, I incorporated the coordinate plane, zero pairs, and absolute value when programming the Sprite to move and show constant motion.
I try to always tie in what we are learning in math to my students everyday lives and to also have hands on activities so they are creating something therefore making the lesson more engaging. I hope that by incorporating computer science in my classroom will help the students apply what they have learned and feel engaged in creating something from their knowledge.