Blog 12 - Looking Back

Over the course of this semester I have grown so much in my thinking about what teaching math really is. I used to teach the way I was taught, and I thought since it worked well for me, that it would work well for my students too. I had to make modifications throughtout the year because my students weren't always engaged. I tried to make tasks more engaging, but I still wasn't teaching math in the Constructivist manner. I taught lessons by showing examples and giving algorithms. Students worked on the task, and then we'd go over the task and I'd offer questions. Students often asked for help, and I would help them rather than asking them to construct their own knowledge. I know that the constructivist manner will be so much better in terms of getting the students to think deeply and make connections to prior knowledge. I learned the importance of Big Ideas in guideing the lesson too. This course has given me a wealth of knowledge to take back to the classroom this fall.

Blog 11 - Overall Inspire Academy Experience

Reflect on the entire experience after teaching the two days in the academy.

I think the esperience at Sandtown was just what we needed. It was nice to talk about these new methods in class, but to actually be able to put them into practice and observe how the students react when made to construct their own knowledge gave us real insight for the future. I was impressed with several of the girls. They really have taken an initiative in math - Lauren especially. She reminded me so much of my smartest girl from last year. I think this method is empowering for both girls and boys. Students can get engaged and bring in prior knowledge to construct new ideas. This is exactly what we saw this week. I'm so glad we had this opportunity.

Blog 10 - Inspire Academy Experience, Day 1

Reflect on the first lesson experiences from your perspective.

I really enjoyed observing the lessons today. It was nice to see constructivism in practice. The students were very reluctant to begin the task on thier own. Each student expressed that they didn't know how to solve our problem. They finally began working and thinking it through and the one that was complaining the most about not understanding ended up being the first one to solve a piece of our problem. One of our students didn't seem to do as well as the others. He began to shut down when he noticed everyone else getting it except him. Other students began to help him though. In the end, students were able to justify their answers and I think this was a great learning experience.

With 5 students I think this approach was easy. Monitoring them was no problem and assistance could be provided if absolutely necessary. I wonder how this would play out in a class of 20+? What if many students were shutting down because they "didn't get it?"

Blog 9 - Expectations for INSPIRE ACADEMY

Blog: Reflect on your expectations and opinions about going to Sandtown Middle School and teaching sixth grade students in the INSPIRE ACADEMY.

I am excited about the INSPRE ACADEMY. I think my group has a great lesson planned for Tuesday and it should really get the 6th graders into Algebra. I expect the students to be really attentive and motivated to learn since they're in a voluntary summer program. I think this will be a valuable learning tool for myself and my group members as well. This will be our chance to take the new methods into the classroom and see how it works before taking it back to our schools in the fall.

Blog 8 - Technology in the Classroom

Blog on a topic related to the course on mathematics teaching and learning.

Calculators, computers, and other technology used as tools in the teaching and learning of mathematics can assist in the transformation of the students into critical thinkers. Technology uses brain power to make students think critically to solve mathematical problems and to apply mathematics in a hands-on manner. I think the use of computers in math classes can enhance mathematics understanding for all learners. Calculators can compute outine calculations, allowing the learner to concentrate on the strategies to solve the problem. Computers can be used to illustrate mathematical concepts graphically and this kind of visual representation can help understanding. Computers can simulate a variety of modeling options, freeing the learner to determine the most appropriate model to use in a given application. I think the more technology we integrate into the classroom, the better.

Blog 7 - Relevance

In class we raised the idea that good problems/tasks should be relevant to the lives of students. What has your experiences regarding the mathematics tasks that you experienced as a student? What about a as a teacher? Do you see relevance as a valid focus for the midddle grades mathematics teacher?

I remember completing a lot of problems straight out of the book when I was in school. Teachers would assign 1-25 odd or something like that. They were typically straight algorithms, few in word problem format. I didn't mind that they weren't relevant or engaging. I still enjoyed doing them. Other students in my classes didn't seem to mind either. We knew what we had to do and we did it. Today, students don't seem to have the same work ethic. They don't really even want to complete tasks that are relevant, so they surely wouldn't have wanted to do the problems I had to complete as a student. I try my best to make problems relevant for students. I make up a lot of my own word problems for them based on events/things they've told me. I'll use students names in the problems. They usually focus on things like music, sports, and other things of interest. I think relevance is so important in math today. You have to make things engaging for students, and part of being engaging is being relevant. They have so many other things like video games and computers that engage they in such high-tech, fast-paced ways, it's hard to compete. So if tasks aren't relevant, they think they'll never use this info.

Blog 6 - Lesson Plan

Discuss your ideas about your first lesson plan and the comments you received. Where there any surprises in the feedback? Were they already in line with your thinking? How does your current philosophy of lesson planning and teaching compare with what you wrote on you first lesson? What changes will you consider?



I wasn't sure what to expect with my lesson plan. When I got it back and looked over the comments, they made sense. I noticed that some of my Big Ideas meant to guide the lesson weren't even Big Ideas at all. I also noticed that I was leading students toward the algorithm by activities utilized in the Before section. I was even focusing too much on the answer rather than strategies and processes and the development of ideas and understandings. There were no suprises in the feedback. In fact, my current philosophy of lesson planning now reflects these changes. I will make changes to take into account all of these recommentdations. My first lesson plan was inadequate in these sectors and changes will reflect the refinement of my lesson in these areas. I'll let the Big Ideas guide the lesson, engage students before presenting the task, focus on mathematical strategies, and assess according to Big Ideas.

Blog 5 - Letting Go

The term Letting Go has been used by Van de Walle and in our classrooms to represent how teachers teach THROUGH problems. Where are you on this at this point? Examing the teaching stations, and your own ideas. Key- When should the mathematics teacher let go and when do you believe it is best to do otherwise?

I think going through the experience of being the teacher in the teaching stations helped me see what it means to let go. I was so tempted to help a couple of my 'students', but remembered to direct them back to their group to talk it through and discuss the issues they were having. I wish I had gotten further along in the 'After' process, but I was able to see other teachers go through that. I think a teacher should always be able to let go. The only time when it Letting Go is not the best option would be when students are having a difficult time with the problem, are getting frustrated, withdrawn, and quit working. It is okay to let students struggle, but when my students simply can't figure it out, you must give hints or help them or they get frustrated and quit. This definitely doesn't help the learning process. Once they quit, it's hard to get them motivated again. So letting go works as long as you're monitoring well and can sense when it is time to try something different.

Blog 4 - Math all around us

How is mathematics used by those in the pubic domain? To address this question, explore the news or print media in the next few days to get an idea of its power to decide. What does this imply for the teaching of mathematics, constructivism, and who can do mathematics?



Mathematics is used in nearly everything. This means that we must prepare every child to do mathematics. Service, business, public, etc...all sectors rely heavily on math. From simple things like making correct change at the grocery store to making complex public and private sector budgets - math is all around us. This has serious implications for the teaching of mathematics. We must ensure that it is being taught in a way that the students learn best. Mathematics must be comprised of meaningful learning. Students have to be able to make connections with events in their everyday lives to make math relevant. Constructivism must be employed. Student-centered classrooms are necessary to foster the deeper understandings required today. Math is no longer teacher-centered with rules and procedures. Students have to be able to construct their own knowledge and make connections among mathematical ideas. Everyone can, and must, do mathematics.

Blog 3 - Limitations to Constraints

What have you and your colleagues seen in the past as "limitations" to the student-centered teaching of mathematics? What is the status of your current thinking regarding these "limitations"? How do you envision "engineering" as a way of shifting thinking from "limitations" to "constraints"?

Limitations of the past included such things as the inability to "let go", insufficient time, parents who aren't involved, students who seem bored or disinterested, insufficient technology, etc. I now see that these don't have to be limitations. They don't have to prevent the student-centered teaching of mathematics. Rather than being limitations, we can design (or engineer) a curriculum where these are only the constraints that we must plan for and overcome. They can no longer be excuses for why we can't teach student-centered mathematics, but lessons must be planned in a way as to overcome these constraints

Blog 2 - Constructivism

Having considered the question, how students learn mathematics through terms like constructivism and understanding, how do these theories and perspectives compare with what you have thought prior to this course? What do you think are the implications for constructivism in the classroom -- what would it look like?

Prior to this course, I thought that an effective way of learning was by using the 'show-and-tell: teacher-directed approach'. This way, the students were shown how the teacher wants the problem solved, and are guided in this manner. The students aren't able to construct their own ideas. No reasons are offered as to why you approach a problem in this manner, rules are assumed to be obvious, and the teacher receives no input on the ideas students have. The teacher can only find out if students are able to follow directions. However, many students who solve the problems correctly really don't understand and will be reinforced that math is a collection of rules to be learned.

Constructivism is much different; it is a student-centered approach. Students are free to develop their own ideas by using prior knowledge to give meaning to the problem solving strategy they develop. Once students have been given time to work on the problem and connect ideas to construct new ideas and develop an understanding, there is a discussion phase where ideas continue to grow. Students may hear new ideas that they hadn't thought of. Teachers begin where the students are - with their ideas. Students are allowed to solve problems in ways that make sense to them by using their own ideas.

Blog 1 - Influence of Past Experiences

What have been your past experiences learning or teaching mathematics and how have they influenced what you said about mathematics teaching and learning in class?

In my group, we defined math as: reasoning, logic, problem solving, and strategy. We came up with this based on past experiences both learning and teaching math. I always viewed learning math as following certain rules, formulas and strategies to come up with the correct answer. But once I began teaching, I relaized the reasoning, logic and problem solving strategies were very important. Math is no longer guided by strict rules. It is much more about relating it to the students in order to engage them so they can be effective problem solvers. The CRCT has very few straight-foward problems. Most of the problems force students to read, think, use reasoning and logic, and effectively choose the correct strategy to solve the problem. Getting away from the "teacher show" allows students to collaborate and solve problems on their own. Students learn by doing.