How should students take notes in a Math class?

               As I was reading through many of my classmates' blog posts, I realized that many of them touched upon the issue of taking notes with technology, and using eBooks or actual books. I would like to comment on the issue of taking notes with technology, either by typing everything on a computer or taking a picture and saving it in their phone. I am not against the idea of taking notes with a computer, but for Math, I believe that students shall actually write down notes with a pen or pencil. I type on my computer to take notes for many classes all the time, but I feel like it is much more effective and easier to actual write down notes with a pencil than trying to figure out how to type sigma in a word document. For math, there are many symbols and notations that you can't really "type." You have to click several tabs in Microsoft Word to insert a Greek symbol or square root, and that often takes too much time. It defeats the purpose of taking notes with a computer if students are wasting time on figuring out how to type all these math notations. Therefore, I believe that students shall not take notes with a computer in a Math classroom. The traditional note-taking is much more effective. In addition, students will be able to retain more information and remember the content better if they actually write the notes. I find that true all the time at my fieldwork site. Whenever my cooperating teacher asked students about an example that they had done before, the students always said something like "oh, I remembered I wrote that down somewhere in my notebook," and they would start flipping through their notebook and know exactly where to find it. As a result, I will strongly encourage my future students to take notes using a pen or pencil.

Socrative

              Coincidentally, I was able to observe an inclusive special education class. I really like how the teacher incorporated technology with Mathematics. The teacher gave out IPads to students, and they logged into a website, www.socrative.com. There was a chat room that the teacher had created, and they were able to do math problems and interact with others via the chat room. The teacher would post a multiple choice question in the chat room, and the students would be able to access it on their IPads and choose their answer. The website would actually tell the students whether they had chosen the right answer or not, and on the teacher’s screen, it would show the teacher what all the students had chosen. The teacher would go on to the next question after every student had answered it. The website also showed how many had chosen an answer, and how many were still working on it. I like how the website actually shows you the statistics or the spread out of the results. It allows teachers to monitor students’ progress, and which question troubles students the most. Therefore, teachers will be able to use the result to make appropriate adjustments in the lesson, and determine whether further clarification or reteach is required or not. In addition, students all are working at the same pace, as a group because the teacher would't go on to the next question until everyone had answered. I will definitely use it in my classroom if I have enough IPads or computers for every student. Students enjoy doing it, and this can be a great warm-up activity as well. 

Collaboration Canvas

      At first, I had a hard time figuring out how to collaborate math with other content area since my unit is so specific to Math. Therefore, I begun to review my classmates’ canvases, eventually choose the Ancient Egypt unit plan canvas to do the remix. The unit focused on the characteristics of Egyptian Art, and this can definitely be collaborated with my unit on polygons because shape is an important element of art. Shapes used in drawings can actually mean something. Therefore, I added a mathematical aspect to the Ancient Egypt unit by first figuring out the grade level that the original unit plan aimed for. The standards actually aimed for both 8^th grade, and 12^th grade, so I decided to align the collaborated unit with high school geometry standards. Since the two units are very different, I added three videos, and images to make the collaboration. I added the study of the Golden Ratio, and Egyptian architecture like the Great Pyramid to the original unit plan, so that students can understand the geometry behind it. I also added images of paintings and sculpture that could be used to study polygons. To connect the two units, I added two new essential questions, and changed the original essential question by adding a mathematical perspective to it. I asked students to think about the importance of polygons in the context of real life, and art. I did not remove anything from the original canvas because it collaborated with my unit pretty well. 

Remixed Canvas: 

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2569&mode=view#network6

How to overcome Math anxiety with technology?

Nowadays, many students may have developed Mathematics anxiety; some are more severe than the others. As the name suggested, it is an anxiety about one’s ability to do Mathematics. If teachers don’t encourage students to keep trying, and convey the message that making mistake is an essential part of learning, students may easily develop anxiety in Math. When students reach the higher level Math classes such as Pre-Calculus or Calculus, they may not realize that grasping the concept require more efforts and time than before, and feel frustrated or discouraged when they don’t get it right away. As a result, I believe that teachers shall try to come up with ways to prevent their students from developing the anxiety, and technology may serve the purpose. Students in the 21th century tend to prefer reading an eBook over an actual book. Therefore, they will definitely want to learn Math even more if they can both play and learn at the same time. There are many educational apps out there that teachers may suggest to students such as Sudoku, Luminosity and the Math Workout. These games are fun to play, but also challenging as well. Most of them require mathematical thinking, and use of logic. Many of them are even free, so why don’t we bring that into our classroom and suggest them to our students? There may be some down time in the classroom, and teachers should just let students to play games like Luminosity rather than making them watch some random videos. This helps teachers to convey the message that learning Math is not hard or boring to students. By doing so, students may regain their confidence, or even develop interests in the subject. Overcoming the anxiety is easy if we can shift gear a little bit, and let students realize that Math isn’t something that hard to understand and useless by integrating educational apps into our lessons. Start off a Monday morning lesson with a Sudoku may not be a bad idea. Students will definitely want to learn it if they see that it is fun, and interactive.

Unit Plan Canvas

         My unit focuses on the properties and real life applications of the most common types of polygons (quadrilaterals, triangles, and polygons in general). Students will explore the sum of the interior angles using the Angle Sum tool on the Illuminations website, distinguish between polygons, calculating the area of polygons, and etc. The biggest challenge that I encountered when I created the canvas was coming up with an essential question that prepared students for the entire unit. The entire unit consists of different sub-topics such as the study of triangles and parallelograms, and don't necessary go along with each other. Therefore, coming up with an essential question that ties the entire unit together became my biggest challenge. Finding the videos and images were easy because there were many useful resources out there. I found a lot of great videos on YouTube and had to actually get rid of some to avoid putting too much thing on my canvas. Create this canvas really gets me to think about the entire unit, and I had to actually "plan-out" the unit by writing down the topics that will be covered in the unit to write my introduction for the canvas, and jot down standards that will addressed. The canvas is basically a layout of the unit, and I feel that this is helpful to students. They may get a sense of what they will be studying before hand. Introducing the unit through a canvas is a good way to get students started. Therefore, I will absolutely use this in my future classroom.

My Canvas for a Unit on Polygons:
http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2281&mode=view#network6

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. 

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