Algebraic Habits of Mind in my lessons: I have already been incorporating habits into my lessons. I’ve taught using inverse operations and/or using the inverse of the constant in UNDOING an equation that is being solved to find the solution for the variable. I’ve shown students how they can take a simple word problem, such as fair tickets costing $2 each, where they can utilize the DOING habit by taking a table they’ve created with reasonable domains to find the range. I’ve also shown them how they can take that same table and, by working backwards, they can write an equation that can be used for all possible independent values. I can further extend this same problem by presenting them with a related situation where they have a certain amount of money and they have to determine the number of tickets they can purchase, input from output. This same lesson also utilized the habit of BUILDING RULES TO REPRESENT FUNCTIONS. They utilized the multiple representations that they learned in previous lessons for organizing information. They were able to predict the pattern of the graph. Using multiple representations of the function allowed for chunking information to assist towards describing the rule for the given situation. They have started seeing that different representations can be helpful in different ways towards finding the desired answers and understand the situation in more than one way. When the concept of slope and characteristics of slope lessons occur they will be describing change. Additionally, they will be justifying the rule, especially when they learn that the domain and range of an equation can be limited by what is reasonable for the situation. My students are being challenged with the habit of ABSTRACTING FROM COMPUTATION in writing symbolic expressions for basic word problems, such as “multiply a number by 4 and subtract 3”, as well as situational word problems where their tendency is to just find the answer rather actually writing the equation used to find the solution. The goal in future lessons is for them to learn that writing the equation for the problem situation is a computational shortcut so that they can find an output for a larger input that would otherwise require lengthy computations. I will repeatedly stress justifying shortcuts, equations or expressions, by testing the shortcut with at least 3 smaller inputs to see if the outputs match the given representation or are reasonable for the situation. Once they have justified their written equations then the value of learning is extended by generalizing beyond the examples they have been working with, typically by using larger reasonable values. Even though they’re starting to see equivalent expressions when solving and checking single variable linear equations or even equations that have the variable on both sides of the equation, the level of rigor for equivalency will increase when the lessons for factoring take place. The lessons where equations are being converted from standard form to slope-intercept form will utilize the habit of calculating without computing.
Algebraic Habits of Mind in my lessons: In my class we are currently transitioning from solving two-step equations to solving multi-step equations. As a result we have been working in the doing and undoing phase of Algebraic habits by solving real-world problems in which they were given the range of a situation and asked to find the domain. As we transition to multi-step equations, students are being introduced to or re-introduced to algebraic proprties. In class the studnets are also transitioning to the building rules to represent functions by being asked to write in thier own words what they observe happening as an expresion/equation is being simplified, solved or both. As they have been transitioning I have put emphasis on having the students think about understanding the process of getting to an answer and not just on the answer itself. I beleive this will help them to develop the ability to create and justify computational shortcuts which is a very critical skill once they move to Geometry and other branches of mathematics.
Algebraic Habits of Mind: My students have practice using all parts of the Algebraic Habits of Mind om class.We have practice using the abstracting from computation while we were solving equations and simplifying algebraic expressions. Some of my students would rather us the a concrete model to solve an equation instead of doing it algebraically. We have done some parallel modeling modeling to organize our process on how to solve equations. During this process it forces the students to justify each step with solving an equation and just the of doing something because I said so. We are about to get into finding the slope and the y-intercept of linear equations. They will be introduced to them by having to find specific data and then predict what will happen if the graph continues at a constant rate of change. Each Friday I have my students to write a journal entry. the journal entry's require may require them to compare and contrast two things or explain to someone how to solve certain equation in their own words. I have also had my students to get into groups and create their own word problems to generate an equation. They then had to solve the problem using multiple representation. As they the year continues to progress I will continue to challenge my students to think more real-world and build their confidence.
My students are using doing and undoing in class and don't know they are using it, I love that fact that they are using this approach and they don't know it, My students are so smart, and I am getting them to use their brain cell and increasing there learning.
So we haven't yet gotten to our factoring piece, but I really enjoyed this lesson. It really fit in with the Algebraic Habits with the process of building and deconstructing the garden. I think that this lesson is one that I can incorporate as is. I also had an epiphany and I am going to try to construct a real "math" garden for the student to work and observe the mathematical principals involved with constructing and maintaining the garden. I' ll let you know if and when it develops.
Algebraic Habits of Mind: In my class we are currently using algebra tiles to solve multistep equations. I started the year using algebra tiles to simplify expressions as well (since we don't have class sets of the algeblocks) so they will be more accustomed to working with algebra tiles when we get into factoring. I am going to try the garden activity from the September 29th training directly after we talk about multiplying binomials. Then we can discuss doing and undoing. How factoring is just a fancy word for dividing polynomials. We works forwards by multiplying binomials, and backwards by factoring binomials. As the students do more and more problems involving factoring, they will eventually see patterns as they discover rules themselves. They could then justify the rules. That lesson really builds the foundation in factoring (something we all know our kids struggle usually struggle with).
Nicole LaraeOctober 27, 2012 11:05 AM We use Algebraic Habits in class with solving algebraic expression. When the students we find the Greatest Common Factor to solve the expression, we worked backwards. We worked backwards first. I gave them the answer and they figured out what I had to divide or multiply to solve the problem. I found that when you give them the answer, they figures it out how they use it.
The Algebraic habits of mind that come to mind is doing/Undoing. This was used in my class to help the students solve equations. In the factoring lesson we did the same thing. Students must know how to do and undo which will help them to solve equations.
Algebra tiles have allowed my students to make a connection between the concrete and the symbolic representations. That has transformed this topic for me and the kiddos. I look forward integrating more great strategies and lessons!
My students are using the doing and undoing with multi-step equations. I will be using the garden activity when introducing factoring to my students. It will increase the rigor in my class and my student's thinking.
The Algebraic Habit of Mind that comes to mind when thinking through the Factoring Lesson from September 29, 2012 is Building Rules to Represent Functions. Students need to understand that there is more than one way to represent and solve a quadratic equation. I am on an accelerated scheduled at my high school and I am currently teaching Mathematical Modeling w/Application only. I had covered factoring prior to our UNT class meeting on 9/29 with my Mathematical Modeling with Application students I am able to utilize the factoring activity (a concrete model -- a picture for the student's mind) during tutorials with student(s) struggling to grasp the concept of solving a quadratic equation using a table, graph, and/or algebraic method.
Algebraic Habits of Mind in my lessons:
ReplyDeleteI have already been incorporating habits into my lessons. I’ve taught using inverse operations and/or using the inverse of the constant in UNDOING an equation that is being solved to find the solution for the variable. I’ve shown students how they can take a simple word problem, such as fair tickets costing $2 each, where they can utilize the DOING habit by taking a table they’ve created with reasonable domains to find the range. I’ve also shown them how they can take that same table and, by working backwards, they can write an equation that can be used for all possible independent values. I can further extend this same problem by presenting them with a related situation where they have a certain amount of money and they have to determine the number of tickets they can purchase, input from output.
This same lesson also utilized the habit of BUILDING RULES TO REPRESENT FUNCTIONS. They utilized the multiple representations that they learned in previous lessons for organizing information. They were able to predict the pattern of the graph. Using multiple representations of the function allowed for chunking information to assist towards describing the rule for the given situation. They have started seeing that different representations can be helpful in different ways towards finding the desired answers and understand the situation in more than one way. When the concept of slope and characteristics of slope lessons occur they will be describing change. Additionally, they will be justifying the rule, especially when they learn that the domain and range of an equation can be limited by what is reasonable for the situation.
My students are being challenged with the habit of ABSTRACTING FROM COMPUTATION in writing symbolic expressions for basic word problems, such as “multiply a number by 4 and subtract 3”, as well as situational word problems where their tendency is to just find the answer rather actually writing the equation used to find the solution. The goal in future lessons is for them to learn that writing the equation for the problem situation is a computational shortcut so that they can find an output for a larger input that would otherwise require lengthy computations. I will repeatedly stress justifying shortcuts, equations or expressions, by testing the shortcut with at least 3 smaller inputs to see if the outputs match the given representation or are reasonable for the situation. Once they have justified their written equations then the value of learning is extended by generalizing beyond the examples they have been working with, typically by using larger reasonable values. Even though they’re starting to see equivalent expressions when solving and checking single variable linear equations or even equations that have the variable on both sides of the equation, the level of rigor for equivalency will increase when the lessons for factoring take place. The lessons where equations are being converted from standard form to slope-intercept form will utilize the habit of calculating without computing.
Algebraic Habits of Mind in my lessons:
ReplyDeleteIn my class we are currently transitioning from solving two-step equations to solving multi-step equations. As a result we have been working in the doing and undoing phase of Algebraic habits by solving real-world problems in which they were given the range of a situation and asked to find the domain. As we transition to multi-step equations, students are being introduced to or re-introduced to algebraic proprties. In class the studnets are also transitioning to the building rules to represent functions by being asked to write in thier own words what they observe happening as an expresion/equation is being simplified, solved or both. As they have been transitioning I have put emphasis on having the students think about understanding the process of getting to an answer and not just on the answer itself. I beleive this will help them to develop the ability to create and justify computational shortcuts which is a very critical skill once they move to Geometry and other branches of mathematics.
Algebraic Habits of Mind:
ReplyDeleteMy students have practice using all parts of the Algebraic Habits of Mind om class.We have practice using the abstracting from computation while we were solving equations and simplifying algebraic expressions. Some of my students would rather us the a concrete model to solve an equation instead of doing it algebraically. We have done some parallel modeling modeling to organize our process on how to solve equations. During this process it forces the students to justify each step with solving an equation and just the of doing something because I said so. We are about to get into finding the slope and the y-intercept of linear equations. They will be introduced to them by having to find specific data and then predict what will happen if the graph continues at a constant rate of change. Each Friday I have my students to write a journal entry. the journal entry's require may require them to compare and contrast two things or explain to someone how to solve certain equation in their own words. I have also had my students to get into groups and create their own word problems to generate an equation. They then had to solve the problem using multiple representation. As they the year continues to progress I will continue to challenge my students to think more real-world and build their confidence.
Hi
ReplyDeleteI had a great time using Alg tiles in class for solving equ. I will be using this in class.
ReplyDeleteMy students are using doing and undoing in class and don't know they are using it, I love that fact that they are using this approach and they don't know it, My students are so smart, and I am getting them to use their brain cell and increasing there learning.
ReplyDeleteAlgebraic Habits of Mind Factoring:
ReplyDeleteSo we haven't yet gotten to our factoring piece, but I really enjoyed this lesson. It really fit in with the Algebraic Habits with the process of building and deconstructing the garden. I think that this lesson is one that I can incorporate as is. I also had an epiphany and I am going to try to construct a real "math" garden for the student to work and observe the mathematical principals involved with constructing and maintaining the garden. I' ll let you know if and when it develops.
Algebraic Habits of Mind:
ReplyDeleteIn my class we are currently using algebra tiles to solve multistep equations. I started the year using algebra tiles to simplify expressions as well (since we don't have class sets of the algeblocks) so they will be more accustomed to working with algebra tiles when we get into factoring. I am going to try the garden activity from the September 29th training directly after we talk about multiplying binomials. Then we can discuss doing and undoing. How factoring is just a fancy word for dividing polynomials. We works forwards by multiplying binomials, and backwards by factoring binomials. As the students do more and more problems involving factoring, they will eventually see patterns as they discover rules themselves. They could then justify the rules. That lesson really builds the foundation in factoring (something we all know our kids struggle usually struggle with).
This comment has been removed by the author.
ReplyDelete
ReplyDeleteNicole LaraeOctober 27, 2012 11:05 AM
We use Algebraic Habits in class with solving algebraic expression. When the students we find the Greatest Common Factor to solve the expression, we worked backwards. We worked backwards first. I gave them the answer and they figured out what I had to divide or multiply to solve the problem. I found that when you give them the answer, they figures it out how they use it.
The Algebraic habits of mind that come to mind is doing/Undoing. This was used in my class to help the students solve equations. In the factoring lesson we did the same thing. Students must know how to do and undo which will help them to solve equations.
ReplyDeleteAlgebra tiles have allowed my students to make a connection between the concrete and the symbolic representations. That has transformed this topic for me and the kiddos. I look forward integrating more great strategies and lessons!
ReplyDeleteMy students are using the doing and undoing with multi-step equations. I will be using the garden activity when introducing factoring to my students. It will increase the rigor in my class and my student's thinking.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThe Algebraic Habit of Mind that comes to mind when thinking through the Factoring Lesson from September 29, 2012 is Building Rules to Represent Functions. Students need to understand that there is more than one way to represent and solve a quadratic equation. I am on an accelerated scheduled at my high school and I am currently teaching Mathematical Modeling w/Application only. I had covered factoring prior to our UNT class meeting on 9/29 with my Mathematical Modeling with Application students I am able to utilize the factoring activity (a concrete model -- a picture for the student's mind) during tutorials with student(s) struggling to grasp the concept of solving a quadratic equation using a table, graph, and/or algebraic method.
ReplyDelete