**Using Social-Constructivism and Technology within the Mathematics Classroom: An Annotated Bibliography.**

**Bos, B. (2007). The effect of the Texas Instrument Interactive Instructional Environment on the mathematical achievement of eleventh grade low achieving students. Journal of Educational Computing Research, 37(4), 351-368.**

This article intrigued me since I teach the juniors that have a hard time understanding mathematics. We also use Texas Instruments in the classroom to help students grasp certain concepts. Because I have enjoyed the studies done and recorded by Beth Bos, I was ready to learn more about a technology I use and see what I can implement in my teaching.

Beth looked at another study done in Texas. In this test there were two groups of students, the controls and the experimentals. The students had to be considered “at-risk” according to the end of the year state tests. These students had the opportunity to use Texas Instrument Interactive Software to learn a certain math concept, quadratics. The students kept a journal on what they were learning and how they felt about using this form of technology. Not only were they using technology but they were working together and testing conjectures together as well. At the end of the study, each student took the state test to see how well they understood the material. What was found was a huge leap in the student’s test scores. They not only understood how to use the technology but gained a deeper understanding of the mathematical concepts as well. Because of this study, more studies will be done to answer questions on using technology in other math concepts and how it benefits the students learning process.

Bos mentions the problem with this study and how it can be considered too small. However, even though it is a small study it is a building block for similar studies that will be done in the future to see how technology can help students that have a hard time comprehending math concepts. I have been in the belief that using technology deepens the understanding of how math works. Students can see algebraic rules, tables and graphs and how they are the same yet different. Seeing a visual connection to math helps students make connections with the rules and what to expect throughout a series. Bos knows more research needs to be done to also change the traditional way of learning, “skill and practice”, into more “process driven procedures” which changes the theory of teaching from behaviorism to constructivism.

**Bos, B. (2009). Technology with cognitive and mathematical fidelity: What it means for the math classroom. Computers in the Schools, 26(2), 107-114.**

We use graphing calculators daily in most of my classes. I was interested in finding out if they really were helping my students understand the concepts in a deeper way. Students love interacting with the calculator and seeing all the different capabilities the device has. However, this is not the reason we use calculators. They are suppose to be devices that will help visualize what the math looks like in a different way then just problem solving. It creates new methods and opens the door to more possibilities.

Technology can be a very powerful tool in the math classroom, if used correctly. Bos points out that not all devices and applications can be helpful to the learner. There are several different kinds of web formats created to help students learn math concepts, some are better than others. It is important to find applications that have high cognitive and mathematical fidelity, accuracy in the concepts that are being learned. It takes much research to find the correct applications that will help and not hinder what is trying to be learned. Misconceptions, or button memorization are just a few problems that can arise if using applications with low fidelity.

This article was very helpful to me. I know I will look back at the tables to see the different fidelity levels and web formats that are ranked high. It can sometimes be easy to teach button pushing but this defeats the purpose of why we use technology and in teaching the concepts that need to be learned. A mixture needs to be put into the students notes. Not only the process within the technology that is being used (button pushing), especially when there are several different processes being learned within a unit, but mainly the math concepts and how it is used within the unit, what the concepts are used for outside the classroom.

**Harkness, S. (2009). Social constructivism and the believing game: a mathematics teacher’s practice and its implications. Educational Studies in Mathematics, 70(3), 243-258. doi:10.1007/s10649-008-9151-3**

Teaching students based on their level of math creates classes that are either excited to be in class and willing to learn, or classes that are full of students that have a fear for math, have given up on math, or put barriers up on learning the subject. I was interested in figuring out what the “believing” game entailed. It was hard to keep my focus on reading because it brought to light new things I could implement in my own teaching.

This article looks at a social-constructivist way of teaching problem solving. It is common among math teachers to judge and find faults within students’ thinking process, if the answer that is given is not what was expected. If teachers look instead at finding any correctness or accuracy within any answer given by students, it can open the door to “teacher moments” and gives the students new confidence in answering questions in math. The process was called, “the believing game.”

I really like this idea. Trying to find some correctness within the answers that are provided by students, we create “teacher-moments.” It may create tangents we do not have time to cover at the time being, but we can go back to it, we can let the student know they are correct to a degree and give that student confidence in solving math problems. We then can go back to that moment throughout the year when we cover similar material. I am always looking for ways to give my students confidence and interest in the topics we discuss daily. No matter if the answer given is what I expected or did not expect, I usually follow up with a question on why or how they came up with their given response. This keeps all students on their toes and ready to think about the process, not just an answer.

**Offer, J., & Bos, B. (2009). The design and application of technology-based courses in the mathematics classroom. Computers & Education, 53(4), 1133-1137. doi:10.1016/j.compedu.2009.05.020**

The more I study different learning theories used within the math classroom, the more I connect with the constructivist approach within my teaching. Through the research I have done, I ran into Beth Bos and really connect with what she has researched and written regarding mathematics. I specifically looked her up as an author I was interested in and came upon this article.

A study was done in Texas using technology-based courses (TBC) within the math classroom. Offer and Bos wrote about the study done and the opinions made by the principal, teachers, and students. There were four parts of the study that were then discussed through surveys. The four areas included: “(1) real-world problems, (2) group work, (3) safe and flexible learning environments, and (4) assessment.” Through this form of learning, students connected more with mathematics because of the use of technology by more than 50%. Other students felt they connected better with math because of the the real-world problems and seeing how math was used outside the classroom. The main problem the teachers saw with this curriculum was the lack of group work the curriculum provided. The concern the students saw was how difficult the work was and how time consuming it was. From this study, researchers will continue with more research and try to fix some of the issues that was found with this particular study.

I gained all kinds of information from this article. The main points I gained were not necessarily what the writers were trying to convey. From the teachers perspectives and what they wrote about, what they did and did not like about the technology based curriculum, I can see new things I can immediately implement into my own teaching and curriculum I use. For instance, leveling my seventh graders so they work with others with similar understanding. This way those who struggle can practice more skill and work together to understand. And those who find math easier to comprehend can work together on more extension work. I really like the articles Bos has written and will continue to search out more of her research.

**Overbay, A., Patterson, A. S., Vasu, E. S., & Grable, L. L. (2010). Constructivism and technology use: findings from the IMPACTing Leadership project. Educational Media International, 47(2), 103-120. doi:10.1080/09523987.2010.492675**

Finding an article that had both constructivism and technology in the same title had to be a winner. The philosophy behind constructivism makes it easy to assume teachers that use this theory would also want to include technology. I was interested to see if my own conjecture was correct or not.

The article looked at a study that was done in North Carolina to promote student-centered instruction. They looked at several different facets of the teachers within their study but mainly looking at which teachers use technology within their classrooms and which teachers use the constructivist approach in their teaching. What they found was most of those who use technology also had a constructivist approach to their instruction. The article explained all the different parts of creating the study; from questions asked, years of teaching behind each teacher, gender, location of the schools within the study, and all the statistics that were made from the data found.

What really interested me was the study found elementary teachers were more apt to use constructivism and technology within their instruction more than the secondary teachers. This is exactly the opposite of my school. The elementary teachers all use a behaviorist approach, without the aid of much technology while the secondary teachers can barely survive without technology and use more of a constructivist approach.

**Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers’ intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71(3), 299-317.**

I am interested in reading other viewpoints on using technology within the classroom. The school I teach at has a strong opinion on the matter; technology prepares students for further education. However, a school I taught at previously has the opposing viewpoint: students should learn how to do all math using paper and pencil; the calculator only handicaps the student. With this said, it was interesting to read a study on this subject.

Pierce and Ball point out there are many barriers when implementing technology within a mathematics classroom. This article looks at a study that was done with over 90 different teachers and their attitude toward using technology within their classrooms. Not only does the teacher’s attitude decide if the technology is needed or helpful to include within the curriculum but also the attitude of the administration and parents. Most of the teachers were very positive about using technology, mainly CAS and graphing calculators. The main barrier that most teachers saw was the cost of the technology. Not only did it take a lot of time to learn the new device, the cost of time, but they are expensive financially. Even though the cost was high, the survey showed most teachers thought it was worth it.

My concern with the article was how the survey was done. They sent out emails to 200 different schools asking for the email to be forwarded to the math coordinator. They took in mind region, age, years of experience and gender. My question is, people who do not agree with technology, would they participate in the survey or just ignore the email? I like the results of the survey, but do not know if it was done in a neutral way to get both positive and negative feedback.

**White-Fredette, K. (2010). Why not philosophy? Problematizing the philosophy of mathematics in a time of curriculum reform. Mathematics Educator, 19(2), 21-31.**

The longer I teach mathematics, the more I see a change starting to take place in how math should be taught. With change comes controversy and frustration among the people who teach the subject in question. Why make changes to something that seems to be working? It worked for us, why not for the next generation? The changes in how we teach math is based on the philosophies of why we teach mathematics all together.

White-Fredette looks at the different learning theories and philosophies of mathematics and how it shapes the changes that are made within the classroom. The three main philosophies that mathematics is rooted in are: social-constructivism, postmodern view of mathematics, and the 20th century explorations of philosophy of mathematics. Looking at where these philosophies came from and why they were created has started a discussion on the reasons we teach math. The groundwork for the three philosophies go back to Platonism, formalism, and humanist philosophies. Knowing what each teacher’s personal beliefs are, help determine their willingness to change or why they are set in the old behaviorism way of teaching mathematics.

Coming from a social-constructivist perspective, this article was very helpful to me. It looked at questions all teachers should answer and gets to the root of why we teach math, who should learn math, and how it should be taught. Researchers are seeing a need to bridge the gap of skill and practice with how math is used outside the classroom walls. However, this is a huge change in teaching method and curriculum that can be used. It is a waste of finances to purchase new curriculum if the staff does not buy into the new teaching method. I have seen this in the city I teach in. The district purchased curriculum that was social-constructivist based, but the staff did not agree with the philosophy and so was unable to make the textbooks work. Therefore, the district had to repurchase new material with the behaviorist approach that the teachers were used to using. This was not only extremely expensive, but stepping back in a forward way of teaching math and preparing students for the future.

Reflection:

I was glad to have the chance to research social-constructivism within the math classroom. Since a majority of my seventh grade students come from our elementary program, they are used to a behaviorist approach to learning math. The switch is extremely hard for some of the students. I’m requiring them to use a brain muscle they have never used before by thinking about the process and how we come up with answers. Parents have no idea how to help their children because they never learned math the way we teach it. They themselves are unable to answer some of the questions because they never had to explain processes to solving problems. Therefore I get into some discussions of concern on the parents part. They do not like the change of philosophy. With a few big words and explanations on positive research regarding constructivism, most parents back down and allow for the changes to be made.

The research I did these past three weeks has given me some ammunition on our program we use in the secondary levels at our school. I really enjoyed the articles written by Beth Bos. She has been researching not only a social aspect in learning math but also using technology and how it helps students understand concepts at a deeper level then without using any form of technology. Overbay, Patterson, Vasu, Grable show the relationship with teachers willingness to use technology and in using constructivism within the classroom. They seem to go hand in hand with each other.

Throughout the research I did there were several studies done that has made me think of how I interact with my students and if there are tweaks I need to make. Teaching in such a small school, there are only two math teachers for seventh through twelfth grades. It is our goal to allow students to swap teachers each year. This means we teach different curriculum each year. This year I am teaching a majority of the struggling students. I am constantly wanting to find ways to give them confidence in a subject area they have struggled with their whole school career. Looking for correctness in every answer and using technology for students to see visual connections to concepts are ways I can help my students feel more and more confident in their work and prepare them for the state tests that have to passed in order to graduate.

Researching for the annotated bibliography really gave me more confidence in the program we use at our school and allowed me to see that we are using the best theory for our day and age in math and technology. Through hard work our students are gaining more confidence in their skills and processes in solving critical thinking problems. Because of their confidence, they are willing to try problems they have never seen before and put effort into new concepts. I love seeing students year after year build on their knowledge and grow in their math skills.