1.What are you excited about
as you look ahead to the Fostering Algebraic Thinking course?
2.What are you concerned
about as you look ahead to the Fostering Algebraic Thinking course?
3.Which of the four
Algebraic Habits of Mind is
easiest for you to connect with after today’s brief introduction, and why?
4.What is one question you
have about the Algebraic Habits of Mind after today’s brief introduction?
1) I am excited to learn new ways to guide my students to thinking algebraically. I’m especially excited to use technology personally and professionally to give students a better understanding of algebra. I especially can’t wait to learn how to guide students to a better understanding of number sense; I find that students really struggle with these basic concepts.
ReplyDelete2) I am concerned about the time it will take to implement the new methods and ideas I will learn in my classroom. I have often attended professional development, learned something wonderful and it has fallen by the way side because I have not had the time, personally or in my curriculum to work in new practices.
3) I find that I am most comfortable with Abstracting from Computations. I insist on students understanding why shortcuts work. For example, when solving for a variable and I multiply both sides by the reciprocal, what does that do or undo? It is important for students to understand that the reciprocal does both multiplication and division, leaving a one.
4) What exactly is Doing/Undoing? Does that include checking answers or something more like understanding the relationship between multiplication and division?
Erin, I agree about the excitement about using technology. Our district bought 5 ipads for every sped department across our district, but our school was left out (for whatever reason). This was unusual because they have always given me all materials offered to the 'regular' campuses. It has been so disheartening to know that the sped kids have been getting to use ipads and apps which can help them fill in the gaps. I feel that the technology, and the lessons to utilize it, will go a long way.
DeleteErin, I agree with your #3. I like for my students to learn the algebraic steps so that they understand the proof behind the shortcuts.
DeleteAlso, in response to #4, Doing/Undoing to me is when you show both directions of a problem. Example, simplifying vs. factoring.
1- I am very excited about learning new and exciting ways to teach Algebra concepts to students who are not motiviated. I want them to be excited about learning new and fun ways to use the math concepts they are learning.
ReplyDelete2- I am concerned about the time it will take to put all these wonderful concepts together. I hope I can remember how they were taught and I also hope that my way of teaching it will be fun and exciting to my students.
3. I think I am not really confortable with any of the of concepts. I would really like more time to learn them and how to correctly use them to benefit all.
4. I think it would have to be what exactly is doing/Undoing also? Depending on how the student asked the question and how I interpert there response it could go either way.
One of the good things about using "doing and undoing" is that when students learn Order of Operations, it makes it easier to show the steps to solving equations if you list the operations that they would do to get the original equation based on the order of operations, and then show them that if they work backwards, they can solve the equation easier. A lot of students get confused about having to eliminate what was added or subtracted first. They want to get rid of the coefficient first. But if they use the concept of working backwards, they will understand why they should start with what was added or subtracted as their first step.
DeleteI am also excited about learning new and exciting ways to teach Algbebra. I also struggle with students that are not motivated. I am certainly willing to learn, whatever it takes. I want them to jump out of their seats with excitement about Algebra. I love it when they argue back and forth about math. It just tells me that they are excited to learn.
Delete1- I am excited about learning a systematic way to incorporate higher level thinking into my classroom. I teach sped, but am responsible for staying as close to the district curriculum for non sped students. It can be a huge challenge. I feel that learning about the concepts will help me better help my students.
ReplyDelete2-I am mostly concerned about being able to deliver what I learn; especially to my more learning challenged students. Their self-esteem is already shot so I feel like it can be a double challenge at times.
3- I feel that I do not know enough to be able to pick which one I am more comfortable with. In my brief introduction, I feel that the 'building rules to represent functions' might be the one that I will be able to be most at ease with. Maybe I will be pleasantly surprised.
4-I am wondering how I am going to be able to help students who are on a lower learning level; what if they can't calculate without computing (abstract from computation), or find different representations (building rules to represent functions. So, I guess my ultimate question would be "How am I going to interpret the 'habits' in a way that I can teach them to my student population?
1. I believe that Algebraic thinking should really start long before Algebra I. I am excited to be able to learn this for Algebra I but also for Pre-Algebra and other middle school Math. This past year the 5E Model was introduced in our curriculum however there was no real explanation of how to use it and what the benefits of this learning method is to the students. I am hoping to develop lesson plans that will use the 5E concept fully and really get the student involved and on the path to self-directed learning.
ReplyDelete2. My great concern is the time it will take to develop lessons and plans to teach using our “new” way of thinking.
3. The habits I connect with most are “doing and undoing” as well as “building rules to represent functions”. Getting students to connect to these processes would really help them understand algebra and any higher level math.
4. As I begin researching this topic, why do some sources talk about three habits and other discuss five habits. Are we going to look at the various ideas behind them all?
I agree with the time it will take to develop lessons; especially when it is new to us. It might feel like we are first year teachers again.
DeleteI am also looking forward to learning how to incorporate engaging components into my lesson plans. I work in a low SES school, and the students are not motivated to learn math, much less algebra which seems even less likely to them to be useful later. I am seeking ways to help them become interested and see that math doesn't have to be frustratingly difficult. Time is always a concern for me, too. Whether that time is the time for planning or the time it will require to execute, time is always running short.
Delete1. I'm excited about learning new ways to improve how my students learn.
ReplyDelete2. Probably my biggest concern is always how to incorporate into REQUIRED curriculum that the district mandates.
3. The Doing/Undoing is easiest for me because that is something I repeatedly use while teaching.
4. How would the algebraic habits line up with Bloom's Taxonomy?
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DeleteI am curious as well with the alignment of Bloom's Taxonomy and/or Costa's Level of Questioning. Deep understanding and retention of a subject like Algebra does not really occur unless you are able to move your students to the highest levels of Bloom's or Costa's. In Bloom's, that high level is analysis, synthesis, and evaluation. In Costa's, that high level is level 3 (apply, evaluate, hypothesize, imagine, judge, predict, and speculate).
DeleteTammy,
DeleteI am right there with you. I am also worried about how to combine what we are going to learn with what our districts are requiring us to teach. Surely there must be a way to do both. I suspect that it will require quite a bit of work on our part. I am willing to do the work if my students respond well to it. Is Bloom's similiar to Costa's? I have always found it difficult to move a student through all the levels. I sure could use some advise on this; lower level is easy but what about higher level?
This upcoming year I will also be teaching Pre-Algebra Honors. I have made a decision to do foundational Algebra questions each time I quiz or test as a bonus. I have taught Algebra over the last 3 years and realized how unprepared students come to me. I really need that Bloom's Taxonomy level of analysis, synthesis and evaluation to kick in before Algebra. I hope to adapt the curriculum to increase these skills.
Delete1. I am excited to incorporate Algebra into my 8th grade pre-algebra classes next year. We often teach ways to "get through" the problems, but many of those methods do not extend into the following year's Algebra I course. I look forward to finding beneficial ways to adapt the curriculum to lead the students logically from one class to the next.
ReplyDelete2. I am concerned that I may get overwhelmed with trying to keep up with the higher expectations of my district and the STAAR exams, keep on schedule with my district curriculum AND try to implement ideas gleaned from XTreem Algebra into my lessons.
3. Doing/Undoing seems to be the Algebraic Habit of Mind that comes easiest for me. This was stressed by my professors in college as being critically important, and I have made a goal of being able to always understand the workings enough to reverse. Until that point, I don't feel that I truly understand the process.
4. My question is: What does Abstracting from Computation look like? I guess I don't really understand the description very well, but only the components individually; they seem somewhat unrelated to me.
* Bonus Question: What is the fourth habit? I only saw 3.
Kelli,
DeleteIn resonse to your #2 - I couldn't agree more! The STAAR exam leaves less than 0 time to implement new ideas and practices.
To #3 - that makes so much sense, now I want to make sure that I am explaining it to my students that way, maybe then they can better understand what we do and why we do it.
To #4 - That is a good question and I thought I knew what Abstracting from Computations was, but when trying to think of a better explanation I began to doubt myself. Now I too wonder what it looks like?
1. I am always excited to learn new concepts and ways to deliver information to my students.
ReplyDelete2. I am always worried about whether the things I learn will transfer to my classroom with any sort of ease.
3. Doing/Undoing is the easiest for me to connect. I love to teach opposites and seeing things done forward and backward.
4. Do you really build any rules in math? To my knowledge, a new rule hasn't been built in a long time.
I understand what you are saying with number 4. The way I took it to mean was students building rules that are new to them.
Delete1. As I look ahead to the Fostering Algebraic Thinking course, I am overly excited about learning how to explain more Algebraic concepts to my students. I am really hoping that this course will give me the confidence that I need to encourage me to incorporate it into my Pre-Algebra class.
ReplyDelete2. I am concerned with the material. I haven't really seen an Algebra I course in quite a few years, I may have forgotten some concepts. I am concerned that I won't be able to implement all of the new ideas with the time allowed in our curriculum.
3. After our brief lesson I believe that I connected well to building rules to represent functions because I can organize information and chunck it together, it helps me to understand the problem better. I can spot change easily as well as predict patterns. I also find it easy to justify a rule.
4. The one question that I can come up with about Algebraic Habits of Mind after the lesson is what is abstracting from computation, not too sure how to generalize beyond examples. I also want to know, is justifying a shortcut explaining what you did and backing it up, or does it go more in depth?
Also, one last and final question, are there three or four habits of mind, did I miss one?
I'm glad that you asked whether there were 3 or 4 habits of mind, because I only saw 3 categories. I tried looking through my notes, but I never saw the 4th one. Is there a 4th, and if so, what is it?
Delete1.I am looking forward to reinforcing and learning more about the algebraic thinking. We need to find better ways to reach our students and have fun while we are doing it, if we want them to be ready for higher levels of mathematics.
ReplyDelete2. My concerns are will I be able to analyze what my students needs are, while teaching them to think differently than what they have been taught over the course of their education.
3. The easiest for me is the doing/undoing (Input from output, working backwards). These were the strategies that have been taught in the past. Our students will need to do this, but the will also have to be able to move to the other 2/3rds of the circle (building rules to represent functions and abstracting from computation).
4. The one question I have will be are my student going to be ready for the change, and if so, will I be able to have them be successful with the new learning style.
I don't think any student is every ready for change. When I converted to the NSpire calculators, the amount of complaints was near never ending. Eventually though, like all new things in the classroom, they got used to new routine.
DeletePlease reflect on the following questions about the April 21 session:
ReplyDelete1. As a geometry teacher, I understand how important algebraic thinking is to solve geometric problems. I am excited to learn more innovative ways to teach algebraic process and getting my students excited about the algebra.
2. My only concern about the course is the struggle on how to effectively translate it over to classroom activities.
3.Reasoning with relationships is the Geometric Habit of Mind that is easiest for me is Reasoning with relationships because it is easy to make connections with similarity.
4.I just need to learn how to apply them more.
1. I am looking forward to the various new lessons we will be looking at because I am always looking for the most effective/efficient way to teach my students algebra.
ReplyDelete2. My concern is the same I have with every PD I go to: How effective can this be when using it with students who have 6th/7th grade skills in my class? How effective will this be with the students counting the days until they drop out?
3. The easiest for me to connect with is Abstracting from Computation. I'm always looking for generalized shortcuts to help my students see that math isn't a big scary machine.
4. At this point, I don't have any questions.
Professional Development always leaves me with so much hope and then so much confusion about how to incorporate and make the new information or strategies work in my classes so I get those spectacular results. I have a similar situation with lower ability students and how to bring them up while teaching at grade level; I had some students testing at 4th grade levels in 7th grade this year... seems like I need some magic fairy dust in addition to some great strategies sometimes.
Delete1. I am excited to learn new ways to engage my students and bring more "real life" problem solving situations for my students to work on. I am excited about the opportunity to share my experiences with the other members of the class and listen to their ideas and experiences.
ReplyDelete2. I want to make sure that I get plenty of opportunities to use the technology that we are using in the class and that I can immediately turn what I get out of the class into lessons for my students, and that they will find the material interesting. I want my students to love Algebra as much as I do, and sometimes that is hard to accomplish because a lot of them do not like math.
3. I actually had 2 that were easier for me to connect with. The easiest is naturally the Doing and Undoing. Working backwards is an easy concept to follow. I also liked the abstracting from computation. I connect easily with symbolic expressions and I can see things in a variety of ways.
4. I'm sure that I will have more questions later, but right now, I do not have any questions. I have a question not related to Algebraic Habits. My greatest curiosity is "when do we get the IPAD, CBR, and NSpire" Do we use them when we're working together July 23 through 27? Will we be given software or any applications that we can take back to our classroom?
Carolyn, your #4 question would be one of my questions, too. I hate going to trainings where they show how to use some technology, but there are no hands on or time for practicing and asking questions when I'm not doing something correctly.
DeleteAs Tammy stated above. I hope we will have the opportunity to use the "technology" package we will be given and incorporate it in our curriculum and lesson plans. I love technology and love to find ways to incorporate it in what I am teaching.
Delete1. I am excited and hope on my journey in this course of "Fostering Algebraic Thinking" that I gain teaching strategies and tools that will assist me with helping my students learn Algebraic concepts that are retained because of deep understanding vs shallow and just for some test.
ReplyDelete2. I am most concerned as I look ahead in this course of Fostering Algebraic Thinking with the time management. In addition, I am concerned about being able to fairly assess students' progress when implementing the curriculum and other recommendation of the course.
3. I think the easiest Algebraic Habits of Mind for me to connect with would be Building Rules to Represent Functions. After a while all the world's a function.
4. I don't think I have any pressing questions at this time.
I think questioning techniques (teacher-to-student, student-to-teacher, and student-to-student), will be critical when aiming to assist our students with the development of their Algebraic Thinking.
ReplyDeleteI completely agree Sherry. I spend a tremendous amount of class time devoted to the students explaining or working on how to explain their answers to each other. I have found that even if they are explaining incorrectly in September, they are pretty good by January. It takes a lot of work to get them to that point, but once they do, almost every student buys into each lesson.
ReplyDeleteI am very excited for the opportunity to learn about new ways to reach students in helping them understand and utilize new ways of thinking.
ReplyDeletePOI am a little concerned about implementing these new ideas and Technologies in my current classes.
I think the easiest concept will be moving forward and backwards.
I have no pressing questions at this time but am excited about the opportunity ahead of us.
Ryan Rowlands
I know that I am that I am way behind in publishing a post, but I was so busy at the end of the school year and have already been so busy in the summer with two graduate courses. I am very excited about this course becuase I am always looking for new and creative ways to motivate my students to be successful and enjoy math. With that being said, I am concerned a little how I can get them to fit into my classroom and keep them going. Over the years, I have had a lot "great ideas" that just didn't pan out or they were not executed the way I had intended them. Sometimes these great ideas I gather from workshops don't always mesh with my students and the set up of our class schedule. It will be interesting this year to see since we are going to have a major change to our class schedule. As for the Algebraic Habits, I had to leave early on Saturday and I have not seen these yet. I will do some googling to find out more information.
ReplyDelete1. What are you excited about as you look ahead to the Fostering Algebraic Thinking course?
ReplyDeleteI am excited about new ways to motivate my students and bringing them more rigorous activities.
2. What are you concerned about as you look ahead to the Fostering Algebraic Thinking course?
I am most concerned with integrating my new knowledge and strategies into my curriculum because time is always an issue and it is so much easier to just go back to the same way you have always done things.
3. Which of the four Algebraic Habits of Mind is easiest for you to connect with after today’s brief introduction, and why?
The Algebraic Habits of Mind easiest for me to connect to is Doing/Undoing
4. What is one question you have about the Algebraic Habits of Mind after today’s brief introduction?
No questions at this time.
1. I'm looking forward to new and exciting ideas to bring into my classroom for my students to enjoy Algebra a lot more.
ReplyDelete2. I'm concerned about implementing this strategies into my classroom and how my students will react to the new strategies.
3. The easiest concept is working forwards and backwards.
4. I do not have any questions right now!!