My students make the transition from concrete to abstract best when they are working collaboratively and engaging problems. When they listen to each others’ thinking it helps them to bridge those gaps. It seems to be most difficult to take focus off of “rules” and instead feel comfortable with multiple ways of solving and understanding. Getting kids engaged with the problem (away from paper/pencil) seems to make this easier. Coding is new to me, so I have yet to discover how this will help my students make the transition.
What’s worked for me in the past?
- the “function machine” idea
- making connections between multiple representations (situation in words, graph, table, equation)
What do my students find the most difficult?
- What is f(x)?
- Using parenthesis to mean so many things! Sometimes they mean multiplication, or function notation, or an ordered pair, or a range, etc.
How do you think programming can help with this transition?
- Not sure exactly; I don’t know programming well enough to draw connections.
- Increase engagement. Most students are more interested in a programming lesson than an algebra lesson.
I LOVE algebra tiles! If anyone knows a good free online version of them, please share.
I will try just about anything if it helps the students to remember the lesson.
I use songs or parts of songs to help students remember various lessons or formulas.
I have used numerous activities to let students learn though discovery.
My students have trouble learning new things because they get do caught in the mechanics of the problem because their basic skills are weak.
I am really hoping programming will help with this.
I will try just about anything if it helps the students to remember the lesson.
I use songs or parts of songs to help students remember various lessons or formulas.
I have used numerous activities to let students learn though discovery.
My students have trouble learning new things because they get do caught in the mechanics of the problem because their basic skills are weak.
I am really hoping programming will help with this.
I am new to Algebra I this year. With early math concepts I have used manipulatives, video clips, visuals and repetition. Reviewing previous lessons helped with reinforcement prior to new material being taught. Introducing programming will give the students an instant gratification if they insert the functions correctly.
I find that I have to re-teach the basics of pre-algebra before I can attempt to instruct them in Algebra I. This video about coding is great for students to get a visual representation of what Algebra really is. I often use visuals in my class so my students can try to make connections.
In the past, I’ve used online graphing calculators. But this is usually introduced after they have practiced with simpler functions.
I think the most difficult part for them is to not make mistakes in their arithmetic or else it brings frustration when graphing functions.
I think programming will be another avenue that can help students transition to learn abstract algebra.
I’ve used graphing calculators and manipulatives like algebra tiles to help students transition from concrete to abstract. I have noticed during the past couple of years that my students are less interested in using the hands on manipulatives and are more into using technology. I think programming can help with the transition from concrete to abstract by showing students the importance of math to make technology work.
I try to focus on the vocabulary as a bridge to connect concepts. This helps when I go through each topic that they have prior knowledge. I am concerned with them being calculator dependent for simple computations, especially not realizing that parenthesis play a big role in accuracy. I hope that programming would help deepen their understanding of abstract to concrete while encouraging them to be efficient and that quality of work is important.
“Making representations concrete and connected”… is why I think programming can help transition into algebra. Programming can help students’ understanding of math concepts more relatable and make sense to them in a directly representative way.
Finding how math concepts connect to the students’ prior knowledge and giving them multiple representations on how to solve problems, I think, is a great way to expand their mathematical minds.
Especially with our student population, I think sometimes as teachers we might assume students understand the English vocabulary, not to mention, mathematical vocabulary, so to focus on vocabulary is crucial, too.
What worked for me in the past: Use Algebra Tiles or hands-on activities, Vocabulary- Student read it instead teacher reading the information. Notes-
Math talk with the caculator. I want students to have a better understanding of what the calulator is doing , not just pushing the button. I think
programming can improve students" analytical skills by thinking about how to solve the problem in more than one way write a thorough plan and use logical reasoning.
In the past, I have used acronyms and other shortcuts to help students with concepts like oh order of operations, subtracting integers and more. I found many of them were no longer useful after a certain grade. So I began to use more technology to help with challenging concepts. We use the TI N-spire for exploration so that kids connect with the information in their own way. Then we add to that as we move forward with learning about the concept. I have found that this helps the concept to be grasped by more students. This is why I feel CS that focuses on functions will help my students understand the concepts.
In the past I have use many different things discovery with calculator, youtube videos, pictures and projects. Whatever works but what works for some doesn’t work for others.
What’s worked for you in the past? I always scaffold and teach on top of what the students already know.
What do your students find the most difficult? Just memorizing the rules for each representation of Algebra.
How do you think programming can help with this transition? Programming will help piece everything together so students can see the big picture, or see the macro aspects of learning math in general.