Transitioning Students

[jnmckay]

In the past, making the abstract concepts of algebra as concrete as possible.

In general students have difficulty applying what they learned in real world problems. I find strategically grouping students in hands on learning activities the most beneficial. I am not sure of how CS will be implemented, but I am hoping it will provide a more concrete representations for the concepts taught.

[jschwartz]

First, or any new or difficult concept, I find that REPETITION is a useful tool for improving understanding. I do not mean that 50 problems is required, but certainly going over 5 or 10 examples that are slightly different and require some new thinking each time is a helpful way to "embed" deeper understanding. For example, instead of asking 1 question that requires 1 process, I might ask students to complete the missing values in a a table.

Second, I also use GROUP discussions to promote explanations and inquiry in a more "student-owned" environment. Instead of 1 teacher responding to 1 whole class, I often divide the class into 6 groups so the students can work on guided problems together and use each other as resources in a more comfortable space.

Third, GAMIFICATION has become easier to use as a motivation tool for students. It can be used in so many ways to promote engagement and attention. So, whatever task you want students to spend more time on. create a way to make a game that students can compete or participate individually.

[reinke]

Transitioning from concrete to abstract is one thing that I personally struggled with. In the series that I taught from this past year, we hardly had any Algebra taught to the middle school students. This new series we are going to have will incorporate quite a bit, so as a "newbie" to all of this, I look forward to having the resources to assist me in helping my students with that transition, myself included.

[jk1]

In the past I have spent a fair amount of time helping students understand the foreign language of mathematics.This includes providing concrete opportunities for student exploration and development of meaning.
I also personally feel modeling a variety process and product outcomes is important.

[slgothelf]

Examples, Modeling and Discovery. Students in groups helping each other. If they are missing a basic understanding, it is harder for them to grasp the abstract.
I know zero about programming so I am looking forward to seeing how this will help the students.

[wwong3]

I often like to use word problems and seeing if students can generate mathematical sentences and expressions/equations. This works for some but not all. I think because math is simply a whole other language that first, they must be taught terminology before they can even begin to dissect a math problem. I have not done any programming before so hopefully this will beer beneficial for my education

[mkmccarthy]

Using concrete examples, making connections, and using manipulatives are ways that I have tried to ease this transition.

Students have difficulties with functions. I have tried function machines, real-life examples, and plugging in numbers.

The concepts of programming are related to functions in terms of input, and this could be helpful as long the programming language is appropriate.

[jaburke]

Examples and students doing. Using the correct terms all the times and repeating the terms.

[amcgowan0418]

I think it is useful to show the concrete and the abstract ideas side by side to show the transition.

[mfelton]

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:

What's worked for you in the past?
What do your students find the most difficult?
How do you think programming can help with this transition?

I have found hands-on and manipulatives to work with my students. One of the things my students struggle with is realizing that the process is the same however the numbers have changed. I think programming will help them realize that process stay the same, that numbers or variables change.

[dsdotson]

Providing my students with multiple representations accompanied by concrete examples helps transition them the work they need to master.

[megangrochowiak]

• When teaching each math unit in my 5th grade curriculum. Manipulatives are very important for all learners and there is no time-limit to how long students should use them and then move away from using them. Students want to work with concrete objects to explore mathematical topics, especially when they move into learning Algebraic topics.

• In 5th grade students find fractions to be more difficult because of the representation of parts of a whole. Often the manipulatives don't seem to fit the fractions they represent. It is often observed as an inverse relationship, it doesn't seem logical that 1/2 is left than a 1/4, because 4 is bigger than 2. When they have the fraction tiles to represent this concepts, you can see the moment of clarity go off for them.

• I think that programming can help my students because they can observe that there isn't always one right answer. There are many ways to get to your final product, and it also provides multiple pathways to problem solving, which is something that I am working on in my classroom.

[ann.fraser]

I have found using manipulatives and situational problems really help students. It gives a context for the y-intercept, slope, input, output, etc. ..

[pfraser]

There are several challenges for students when transitioning from concrete arithmetic to abstract algebra. I teach at a high poverty/high ELL school, and the majority of my students have gaps in their arithmetic knowledge that makes the transition to abstract extremely difficult. I use some discovery activities that connect a situation to a drawn pattern, a table, a graph and a written explanation of how the 10th step of the pattern would look (they usually only have to draw the first 5 steps). All of my students can be successful with the first part of this task. Then the students try to find a rule that would always work for any step (n) in the pattern. The exploration during this activity allows discussions about proportion, variables, linear vs non linear, and it has a low access point with a higher ceiling for my advanced students.

While I like the activity I described, many of my students are not successful with the transition to abstract thinking as 7th graders, and I often question whether it is even developmentally appropriate. However, that is not my choice to make and I welcome anything that will engage more of my students and help bridge the gap between arthmetic thinking to abstract mathmatics, and I believe that we can use programing and the resulting concrete actions on screen to do that.

[Mathteachergirl]

For me I have found that connecting to an arithmetic concept students understand helps them extend to the abstract of algebra.

The more abstract a concept the more difficult students usually find it.

Programming is typically very sequential and laying out sequential steps to get started solving a problem can be beneficial for many students.

[tjeaton]

Using as many representations as possible. Concrete examples, pictures, ANYTHING that will carry the concepts. My school has been very limited technologically in the past, but now every student is going to be assigned a chromebook for the year. I'm very excited about the possibilities!

[Lunna]

I used their prior experience arithmetic algorithm side by side to the abstract concept of algebra so that they can be able to connect.
I also involve interactive websites and algebraic tiles as well as various videos.
However, solving multi-step equations, and applications of the concept and skills is a challenge.
I can tell how programming will help after learning and collecting data on its implementations.

[cumminsc]

One method I have used is Algebra Tiles. It is a great visual model to represent how to solve an equation. It makes it easy for students to see that they need to do the same thing to both sides of the equation. I think what is most difficult is when we move into fractions and inverse operations other than add, subtract, multiply and divide.

Programming is a process and just as the video showed, I think it can be good to see the process of writing a code which can also be a process of solving an equation.

[sbaker]

Transitioning from concrete to algebraic reasoning is especially difficult as not all learners are ready to process abstract concepts at the same time. I have found success in using hands on approaches and trying to get students to recognize they have been doing "algebra" much longer than they realize. When students are able to break through self imposed barriers and attempt the math, they find success. As I have been able to positively reinforce correct mathematical reasoning, students flourish and enjoy the process of algebra.

[isitth]

What has worked for my students in the past is exploring a real-world problem that has a patterned relationship. For example, I usually do a matchbox racecar experiment. Using a ramp, big textbooks and matchbox cars, we measure the distance traveled by the car as the ramp is raised. Student collect data on the ramp height and the distance traveled, graph the data, select two points and then create a linear expression. This has been a lot of fun in the past. I would like to have fun again but now I would like to help students see (a) why this is algebra and (b) how this idea could be used in another setting to help solve a problem. There are a lot of cool resources and problems out there. Since I'm now teaching algebra instead of pre-algebra I think that the connections need to be very intentionally made, either through student-to-student discussion or class-to-teacher discussion.