Saturday, October 26, 2013

Scripted Instruction

When I was researching online and deciding what to write about for this week’s blog post, I came across a very interesting article called “Winning Equation: How Technology Can Help Save Math Education.” The article starts out with a powerful statement about the current math education in the United States. It says “Math education in the United States is a broken system.” I kind of agree to the statement and that one simple sentence explains why many students are currently struggling with basic Algebra. Although we know that many students are struggling in Math, but we don’t know how to deal with the struggle. Educators suggest that incorporating technology into the classroom may help. For example, the article suggests different online programs such as the Assistment Program and SimCalc that teachers may incorporate into the lessons in order to keep the lessons current and their students engaged. I agree that those programs may be helpful because we are now living in digital age, where many things can be accomplished through technology. We used to learn Math through lectures and practice worksheets. The teacher would talk and write notes on the board, then go over a couple of examples on the board, and that was it. But nowadays, students don’t like that since they are all being exposed to different technologies outside of schools. In order to make the learning experience meaningful to students and help students see the purpose of what they are learning, we need to relate our lessons to their daily lives. Therefore, I believe the need to make our lessons relevant to students’ lives is the biggest reason why the current school system continues to push teachers to incorporate technology into their classrooms.

Although those programs claim to help students to learn Math, but there are negative effects that the educators fail to consider when they suggest to integrate technology with Math. Teachers will tend to let the program to “guide” the curriculum or pace of the class. Once they have the program in the classroom, teachers tend to build their lessons around it. Teachers should be the one who is making the decisions such as what and how to teach according to students’ needs, not the program. Therefore, schools should be conscious of what program they are bringing in to the school and how teachers are using them. Those expensive programs shall only be a supplement to the curriculum, and not the curriculum. Also, giving online homework through educational websites such as WebAssign may not always be useful to students’ learning. It just makes the teacher’ life easier, and has no benefits to students’ learning at all. Students may make an educated guess to get the question right or work from the answer because students may find pattern in the answers once they have done enough of the problems. I remember that I used to purposefully get the question wrong for the first attempt, and then let the computer to show me the answer so that I can work from the answer to get the same question with different numbers right. Students can always find tricks or other ways to get things right when it is given online or through other technologies. Therefore, we need to be careful with how we incorporate technology into our lessons. 

Sunday, October 20, 2013

Technology & Pedagogy

          By analyzing the lesson plan, I realize that teaching strategies and technologies used in the classroom have to directly support students' learning. I choose the lesson plan, "Adding it all up" because it aligns with the Common Core State Standards and NJCCCS, incorporates technology into the lesson and has clear learning objectives and goals. There are no gap between the curriculum goals, standards and teaching strategies. The lesson uses different teaching strategies such as class discussion, group works, and lecture to address the learning objectives and goals. The curriculum goals are perfectly aligned with the state standards as well. For example, having students to come up with the sum of the interior angles of a polygon formula (sum=180(n-2)) on their own addresses one of the Common Core Practice standards, "reason abstractly and quantitatively." Students first have to draw different polygons, use actual numbers to calculate the number of triangles that can be drawn in each polygon and the sum of its interior angles, and use that information to make conjecture about the sum of the interior angles of the polygon with n number of sides. Students reason quantitatively first and then use what they observe to reason the same problem abstractly. The Angle Sum tool aligns with the lesson because students are able to draw different polygons with different angle measures using technology and see what happen to the angles and angle sum. Drawing polygons with different angle measures by hand can be much more challenging than the actual task itself. Therefore, the Angle Sum tool is in perfect alignment with the technology standard in the NJCCCS and absolutely essential to achieve the curriculum goal. It supports the learning objective by letting students to explore the topic first, and then use what they have come up with using the Angle Sum tool to form a conjecture about what they think is true about polygons with different number of sides and angle measures. The lesson requires students to use inductive reasoning, and the Angle Sum tool clearly supports that.
          Although the lesson plan is well-written in terms of its alignment with the standards, I would like to add something to the lesson plan if I am going to teach this lesson to my students. I would probably let students to share their answers at the end rather than go over the answer with them as a class. I want students to confirm each other's answers by either defending their own answers or refuting other people's answers. In order to do that, students will have to show a deep understanding of the lesson. Therefore, I believe that the addition is necessary and will definitely help to improve this lesson plan.

Spreadsheet:
https://docs.google.com/spreadsheet/ccc?key=0AsoaTIT87eE1dG1WM2RzVTZrZk9xMmE4M25EdUFRVUE&usp=sharing

Saturday, October 12, 2013

Integrating Technology into a Math Classroom

              After the Common Core State Standards has been adapted, more educators emphasize on the use of technology in the classroom and begin to shift from traditional lecture-based to interactive and integrated curriculum. Web-based resources and computer software such as GSP (Geometry Sketch Pad) become popular and more teachers begin to integrate them into their lessons. From what I have learned from all of my education courses, I come up with the conclusion that many students do not like math or can’t see the purpose of learning it derive from the lack interactions between students and teachers, and irrelevancy between the content and students’ lives. When I was in high school, my math teachers would just write notes and formulas all over the board, and then give us several examples to work on. That was the lesson, and not much interaction went on during the lessons because everyone was just busy copying down the notes. Without relating the content to students’ lives, students will not see the purpose of learning it. Online resources such as the free interactive learning sites called the Illuminations are capable of making the abstract content more accessible and relevant to what students experience in their everyday lives. Students are able to explore how completing the square works using the Algebra Tiles application, and graph quadratic functions using the graphing tool. As a result, I strongly believe that integrating technology into the classroom can definitely improve mathematics teaching, but the key is that making a successful transition is hard. Writing notes and formulas on the board is how many teachers used to teach Mathematics for the past twenty years, so it is often hard to change if they lack the knowledge that we have now about the use of technology in a classroom. Therefore, I think the key to make that transition is to educate the teachers on how to integrate technology effectively into their lessons first. Otherwise, all the effort that was spent on bringing in technology such as the SmartBoard into the classroom is just a waste of money and time. I have observed several different math classes already, and realized that the SmartBoard is nothing more than a piece of furniture for decorative purpose. Therefore, we must educate the teachers first in order to guarantee that students will have a meaningful and interactive learning experience. 

Sunday, October 6, 2013

Teaching Machines or Teachers?

           Both the video and article have mentioned a “significant” technology that has had an impact upon education back in its time, which is the teaching machine, invented by psychologist B.F. Skinner. According to the article “A Social History of Media, Technology and Schooling,” the teaching machine is “basically a punchboard that contained multiple choice test items and the machine would evaluate the students’ responses and repeat the answers until the student selected the correct one” (Domine 4). Based on my prior knowledge about the teaching machines and the article, I come up with the conclusion that the teaching machines are not designated to foster active learning, but rather to produce passive learners who are looking for patterns or tricks in the answers. The teaching machine reminds me of an article that I read before for my method course. The article talks about how an educational program called the IPI (Individually Prescribed Instruction) Mathematics does not work out in teaching basic math skills such as performing operations on fractions and decimals. Students in the program work on math questions on their own, and then the teacher will check their answers using an answer key. One student in the program got through the program by making up his rules for operating on fractions, and the teacher even considered him as one of the advanced students. I realize that the teaching machine and the IPI program are similar in terms of the way it “teaches” the content to the students. Both of them do not really require a teacher, and students are basically “learning” on their own. The teaching machine is absolutely ineffective in teaching Mathematics because similar to the IPI program, students can look for patterns in the answers or use trial and error to get the question correct without understanding the concept. Also, what students end up develop is trial and error skill through drill and practice, rather than critical thinking and problem solving skills. Help students to develop conceptual understanding is the emphasis in teaching Mathematics. I am glad that the teaching machine is no longer in use. I really can’t imagine how students can learn Math using it. In Professor Domine’s article, the interviewee Grace described the teaching machine as “a piece of furniture” (Domine 4) and I think that is a perfect description for it. Even teachers such as Bessie at that time did not like the idea of teaching machines, and chose to ignore them.

            Rather than saying that the teaching machine was designed to help students learn or reduce teachers’ work load, it was designed to produce robot-like passive learners who learn the content through repeated exercises. Although math skills can be improved through repeated practice and exercise, but Math is not entirely about drill and practice. The purpose of teaching math to students is to help them to develop problem solving and critical thinking skills that they can apply in other areas as well. The teaching machine obviously can’t accomplish that since you have unlimited tries to guess the answers, and no thinking is really involved. Therefore, I do not think that the teaching machine is an effective technology in teaching Mathematics.