Is Scratch easy to learn? Are we going to learn about it in this CS in Algebra PD?
I find that when I can relate something to the real world that students gain a better understanding of the concept because they are able to see how it is used outside of the classroom. The biggest difficulty by students have is explaining their work and why their answer makes sense. I hope that computer science will make concepts easier for students. I hope that they can relate it to their life and I hope that it will force them to take their time, show their work, and explain understand their work.
Concrete examples motive the need to algebra models. Concrete examples also help student connect algebraic solutions with context (something that my students typically struggle with!)
I always try to connect the lesson to real world applications. Learning CS and Coding not only is a real world application (ie Cell Phones, Computers, TVs, and countless other electronics and devices) but also an exciting and significant sector of our nationās and worldās economy. It not only serves as a vehicle to teach students Algebra, but gives them the opportunity to be ready for a future in the CS Industry
While watching the video, I realized that I havenāt taken time to explicitly show students how their mathematical learning is changing when they begin Algebra. I think that taking the time to do that would really help students change their thinking when approaching the class. I think that sometimes I make the concepts too concrete and that causes students to lose sight of the abstraction.
Currently, I am insecure about using programming to teach mathematics ā I donāt feel that I know enough about programming to handle cases when the language doesnāt fit what I know about mathematics.
One thing that has worked for me is rather than explaining to them what a variable is, doing an activity that builds to the need for variables. I use āThe Border Problemā in which students recognize how to find the number of small squares that form a border of a large square if they have a concrete number on each side without counting the entire border. Eventually it leads to an unkown number on each side and building to the need for variable to make a rule. It is difficult to explain, however I think I quiry works well here rather than just an explanation.
I am not sure how computer science will help as this is very new to me but I am very excited to earn as I redognize students will love this approach to mathematics.
Actually,for my students I think that often they are āafraidā of mathematics and the word algebra. This is too hard for them. They really enjoy programming and computers. I think that if they can see how algrebra has uses in computer science and how something they enjoy utilizes mathematics it will go along way in creating an open mindset for my students and allow them to struggle through and work at concepts.
I always allow my students to graph system of equations before I teach them how to use the different methods of solving systems. Once they come up with the different coordinates when the two lines intersect. I ask them to check their work. I try to make them understand that system of equations only has one answer for x and y. This is my way of helping them see the concrete before they progress into abstract thinking.
If the students find it easy to give directions to their peers on how to complete a task in Algebra- using the concrete methods; I think it will be easier for them to write a program in CS that will work.
I looped with my kids last year and it was really interesting how students who struggled with abstract concepts last year were more successful this school year. I do think that developmental levels are important to consider when creating a lesson. One thing that worries me about using technology is that some students still need to physically manipulate things to understand OR to be engaged.
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One of the best things to do in order to transition from concrete to abstract is to ensure that students understand the concepts in their own terms. Once they have that understanding, then they can understand the abstract. Sometimes, using real models and different visual or activities is what helps students understand. Programming, can help students achieve this because they are going to use their skill in math to apply them to something that has meaning. Many times in math, there is no real application, and through virtual application they will have a better understanding than just solving problems.
I totally agree with you that sometimes what students need is to grow developmentally. All humans grow and develop at different stages and some kids just need some extra time.
The whole concept of solving equations can be difficult and to abstract for many students so I use algebra tiles to help make this abstract construct more concrete.
Once they understand single variable equations they find multi variable equations extremely difficult for most. Iām not really sure how programming will help but I hope to find out.
I use a timer, music, and countdowns to transition my students.
I am not sure how programming will help with transitions but I canāt wait to find out.
I think programming will help students transition from the concrete to the abstract. Programming forces one to understand how to do the problem, so that they can then generalize a solution.
I teach 6th grade, and itās usually the first time students start using variables on a regular basis. Mostly to represent relationships between two variables in a table. Iāve had success by coaching them to describe the relationship in words first, and then looking for words that can be replaced with numbers, symbols, and letters. I think programming can deepen this understanding as they connect commands and group them into functions.
My students have struggled with manipulating variables into equivalent expressions, or recognizing that unlike terms represent different things; for example, recognizing that 5x+3 does not equal 8x. Perhaps the separate blocks for each step in a program will help them conceptualize ālike termsā.
I teach 6th grade, and itās usually the first time students start using variables on a regular basis. Mostly to represent relationships between two variables in a table. Iāve had success by coaching them to describe the relationship in words first, and then looking for words that can be replaced with numbers, symbols, and letters. I think programming can deepen this understanding as they connect commands and group them into functions.
My students have struggled with manipulating variables into equivalent expressions, or recognizing that unlike terms represent different things; for example, recognizing that 5x+3 does not equal 8x. Perhaps the separate blocks for each step in a program will help them conceptualize ālike termsā.
Teaching students that data can be represented in four different ways, as a story, table, graph (or chart) and a rule helps. One of the best strategies for me was to create six different stories, tables, graphs and rules in Excel, paste them in Word, print them, cut them up and put them in envelopes. Then students working in pairs or groups had to match the stories to the table to the graph and the rule. Hugely engaging, thought provoking and led to great discussions as students made the connections.
I think programming would help as it moves students into a sequential arena and from horizontal work representing data on a table top to representing data on a vertical plane. Until students realize everything lies on a coordinate plane, they donāt get the move from horizontal to vertical. Itās weird but they just donāt think about it.
Using this type of program will make the students make sure that their work is correct and if it is not then they need to go back and fix the problem.
This is my first experience in teaching CSā¦ I am hoping this course will allow me to learn about my own skills so that I can facilitate my students. It is my hope that my students will see a purpose for learning algebra and to remember the skills they have learned.
All of the different representations of functions can all be connected to concepts that students have already seen. I always take a lot of time with my students on functions and make sure to tie every representation to something they are familiar with.
My students find it difficult to see the connections between all of the different representations.
Programming is just another way for students to see abstract concepts in a visual way. Any different method to introduce this to students will be helpful!