I feel most students that struggle with algebra feel there is no connection with what they are learning and what they will need to be successful later in life. Therefore there is no real reason in their mind to learn the concept. I feel that in order for students to be able to successfully use programming you need to have technology resources that are consistently working and up to date.
I like using hands-on equations to emphasize the equality concept and balancing the equations. I find this very helpful for equations with variables on both sides. I still find it difficult to get students to transition from the idea of removing materials from both sides of their hands-on equation scale to using mathematical inverse operations to get the same job done. I think programming helps build the logic needed in mathematics - the need to get something to work.
I am a special ed teacher, and I frequently use visuals and manipulatives to teach concepts at a concrete level. When I move to more abstract problems, they have a better foundation and concrete examples to expand upon.
I have found that my students have trouble transferring what they have learned in past mathematical concepts to the next step of the concept. They struggle to see the connection. I try to encourage them to keep practicing and give it a little more time and it will click. I feel that we have so little time to spend on each lesson that the students aren’t really allowed to explore and get enough hands on activities. It is exciting to see it “click” for them.
Relational thinking is really critical here, students need to really understand that math is symbolic and represents something. I don’t have any tricks for this I’m new to teaching math this year and hope to gain insight from the other participants. I do think that programming will help students in that code is symbolic as well, also it performs a function. It is math really, which provides deeper relational thinking.
I struggled with algebra because I couldn’t see the connection to real life, I am very much a big picture to small details learning, and often math works from small detail to big picture.
Teachers at the school where I work have used a three tiered developmental progression with students when learning and applying math concepts - enactive (some might call this using manipulatives), iconic (representing ideas with pictures or models) then symbolic. We try to not ignore the enactive and iconic at the older grades (6- 7 8) because we believe these processes are the bridges to the symbolic (abstract) representations of problems. We feel this progression helps strengthen student’s conceptualization of math processes. Does it always work, no, but students come away with multiple ways to approach problem solving.
This short video cautioned the viewer to make sure that the technology being used really matches the math we desire to teach. I believe that many of our students do need to go back to the concrete example before they can work to the abstract level of math. It is interesting to think that we often teach students that the goal of a math problem is to find a solution. No wonder many students are focused on getting the right answer but fail to see the importance of showing the process of getting this answer.
My students often struggle with being able to explain the concept even if they can do the process. I too hope computer science may help them develop ways to explain their thought process.
Melissa states"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 agree many students need to go through this process but I have also seen that not all models are helpful to all students. Sometimes it is okay to tell a student that it is okay not to understand this model instead to direct them to another model that may be more clear for them. Thanks for reminding me that many students need to go through a process before they can master it.
This is will be my first year teaching 6th grade Pre-Algebra so I’m a little unsure about specific problems my students will find difficult. However, in my technology classes I have seen students figure out how to make things work the way they want to by writing simple equations on scratch paper and figuring it out for themselves.
I agree that programming is helpful because students must correct errors before the program will work. It is also helpful that they know there is an error and can go back through the steps to find this. On a typical math assignment, many of my students are okay with getting something wrong as long as they are still getting an average grade. They are also hesitant to show their work and just want to write down an answer. I think that programming shows them the importance of demonstrating each step, so that if they do make an error they can go back through the solution and find it. Or, I as the teacher can spot the error and I am better able to help.
I’m excited to see how CS can help enhance my classroom. I want the to realize that they think abstractly all the time, but when I ask them To do it, they freak out!
I loved tying everything together this year. Just like in the video, I may have taught each step separately but in the end, my students were able to graph, come up with a table, come up with an equation, and do a mapping. All showing the same thing. The best part was that each student was able to choose the method they preferred and then work to the others and, besides mappings, they all were proficient at one method to start with.
I hope that the computer programming doesn’t end up messing with the rules like the videos showed. Otherwise I’m going to lose the integration.
It’s tough for students to make that transition between concrete and abstract. I try to use visuals when I can so help students “see” math in ways that make sense to them.
I believe the effectiveness of using software in education. In the past, a student would simply solve problems from a textbook not understanding why they did some problems incorrectly. Now, if the software is good enough, it can guide the students through the steps in solving algebraic problems. With a constant feedback system, the student will be able to isolate and understand their mistakes.
This is my first year I will teach Algebra, however I feel the program will benefit the students. My students have difficulty in knowing what is expected in a word problem.
I hope that computer coding will help some of my students
I think the use of manipulatives, seeing real world connections, experiencing productive struggle, and encouragement from the teacher and peers helps with the connections.
To help students transition from concrete to abstract concepts, I try to find ways to relate the concepts to things students are familiar with and have background knowledge… sports, music, money, etc… I also encourage them to draw and label pictures, make tables, and draw graphs.
Students struggle in double checking their work and asking themselves, “Does this answer make sense?”
I think that programming with help students understand the importance of double checking their work… it they do it incorrectly, they will not get the result they expect.