Engaging Students with Concept Mapping Activities

One way that concept mapping can be used in the mathematics classroom is by using a process map to explore types of problems that students are struggling with. A good example of this is adding and subtracting fractions. I had to teach this lesson during my 317 practicum, and I think it would have gone much more smoothly if I had been able to work with students on a concept map like this. It allows students to see a “road map” to solving their problem, and will help sort out and categorize the different steps instead of seeing them as a great big jumble.

Another idea that I have seen implemented in many classrooms is the use of tree diagrams when discussing the outcomes of finite solution systems, specifically as they relate to probability. Most students, when first introduced to the concept of probability, have had to fill out these charts. Usually, the kinesthetic process of hand-drawing a tree will help students to internalize the concept, but for instructors who must make examples for handouts or overhead slides, the automated creation tool for these might come in handy.

I think that it would also be great to have students connect the topic of a single chapter (or even a subject on the whole, i.e. Geometry or Pre-Calculus) to their own lives. This would be an opportunity for students to create a high-visual impact poster that organizes and connects their thoughts and feeling about math with other areas. Since math is an area that students often struggle to connect with, this would be a good way to introduce them to ways that math is relevant to their lives.

Here is an example of a process map for factoring a polynomial:




I think that the main impact of using concept mapping in a math classroom would be to help students to map out and quantify the thought processes that they use in order to find a solution in a given situation. Since math is not about individual answers, but instead about the process you used to find the answers, this is a useful tool to students struggling to understand the steps in the process. This act of drawing out the diagram is a great way to help students who are more visually or psycho-kinetically oriented, since they specifically are the students who are most likely to struggle with the traditional lecture format.

Since time in the classroom is so often limited, it is important to think about which lessons would benefit the most from the addition of a concept map. I think two questions that I would have to ask myself before introducing the concept map activity to students would be whether or not this is going to significantly benefit students' understanding of a topic (if students are already understanding a topic with minimal difficulty, then a concept map activity would be superfluous to their learning), and whether or not the understanding of a topic (or process, as the case may be) would be better served by a different activity (many aspects of math are better quantified in ways less related to words; for example, something like fractals or tesselations lend themselves easily to art projects, whereas if you asked a student to describe the concept to you in words, it would be far more difficult).

Reflections on Using TeacherWeb

1. Describe at least 2 ways that the use of a class web site like TeacherWeb could be used to support your future teaching. Provide some specific details for each example.

Two very helpful things that I could see myself using TeacherWeb for are keeping all homework assignments and due dates in a single place, and allowing parents to access their students' grades online. In the Class Calendar section of the TeacherWeb site the I created, I came up with some example homework assignments that I might assign, and gave the day that they were due. This would be helpful for students who might not be as organized, and may need reminders for project due dates and the like. The Class Grades section of the site would allow parents and students alike to access their current grades and assignment scores using their student ID number. This would allow parents who are concerned about their student's progress to see exactly what their child is missing, and to help keep their child on track. Since the grades are already online, it would not require extra time or effort on the teacher or parent's part.


2. Identify 2 ways students could use a class web site like TeacherWeb to enhance their learning. Provide some details for each way identified.

For some students, it is very difficult for many students to find resources that are freely available to them that will help them with their studies. Doing a web search of "homework help" brings up a slew of results, only a few of which may be at all helpful. With the Web Resources page on the TeacherWeb site, teachers can direct students to websites that will help them with specific concepts in relation to the class. Also, if a student misses school for some amount of time or loses an important piece of paper, it is easy for them to check the Class Handouts section of the website and be caught up with the materials and information that were provided in class. Instead of having to wait and catch up all at once, a student that is absent or disorganized can easily keep up with the rest of the class without additional accommodation.

Blogs and Wikis in Education

One interesting thing that wikis are being used for in education is the long-term collaboration of students in different parts of the country on similar subject matter. One wiki hosts an ongoing joint project between students in New York state and Perth, Scotland. Students collaborate on reading material and share thoughts and notes with one another on their reading.

Another wiki uses a message board system to facilitate conversations between AP and IB students across the country. Some schools require their AP students to contribute to the wiki, but many others contribute out of curiosity for the subject matter, or to be able to better understand things they are confused about. This allows students to share new ways of thinking about topics in an informal, peer-to-peer setting, that for many is less intimidating and more familiar than the "lecture" format favored by many teachers.

Thirdly, some wikis support update widgets, that allow students and teachers to monitor the newest topics and changes made to the wiki from a mobile device. This can be a useful tool for teachers and administrators of wikis because it allows them to better monitor students' involvement, and to prevent unwanted activity.

RSS aggregators are a useful tool for classrooms, because it allows teachers to add reading to their personal websites as it accumulates, without having to seek things out specifically. Students can be directed to a single page to peruse informative articles rather than to several disparate sites, which can cut down on time and frustration for both students and educators. Also, if teachers have information they they are putting online, they can distribute it to their students via the students' own individual RSS feeds, so assignments and due dates can be instantly accessible.

Two pros of using wikis and blogs in education:
-The high accessibility for many students and teachers, and the direct involvement in the curriculum and discussion that this affords.
-Highly varied information sources readily available through links and feeds.

Two cons of using wikis and blogs in education:
-Not all students have access to a computer, and with public libraries and other institutions that would have computers freely available cutting back on hours due to funding, it may be difficult or nearly impossible for some students to access web content.
-Many people take the internet less seriously than they would things in the real world, and the anonymity that the web affords them is in some ways an open invitation to vandalize and destroy work that others have done.

Multiple Intelligences Assessment

The Intelligence Aspect that I scored the highest in was the "Musical" (also referred to as "Rhythmic") intelligence. To me, this assessment makes a lot of sense: my grandmother was a piano prodigy when she was younger, and composed a sizable body of work during her lifetime; both of my parents play instruments, and actually met when they were in a rock band together; and my mother recently made the comment to me that if she ever wanted me to learn something as a child, all she had to do was sing it to me. At the time, she brought up a song that she had taught me in kindergarten to remember my address. I promptly sang the exact song back to her (although I learned it when I was 5 - that's 18 years ago, now!), much to her surprise.

I have a strong habit of playing with words, especially those that form an interesting cadence, and very often compose new lyrics to songs both for fun and to teach myself or others something. These are all common characteristics of Musically Intelligent people, along with easily dancing to a rhythm, playing an instrument, and being distracted my music or ambient noise, all of which describe me very well.

Some technologies I would love to play with that would be helpful to these learning types are music editing programs, so students can see the sound waves of songs that they enjoy and see how it relates to mathematics. I would also love to have students play around with a simple music creation programs on the computer, so they could see how pitch and tone change the feeling of a piece. I also believe that having students write their own songs or lyrics will help them to remember the material they cover better. If the entire class created songs on a particular subject it would be nice to make a CD of all the students work at the end of the project.

In order to accommodate these types of students, I find it very important to keep the classroom at an appropriate level of noise (i.e. if I am talking, no one else should be talking; if people are working together there should be only a medium amount of talking); I like to create rhyming or sung mnemonics so students can remember tricky facts; I will try to integrate art and music into my classroom; and I will seek to find new ways for students to make connections between my subject and the subjects they find in

I believe that being aware of all different types of intelligences will allow students to better use their minds and memories, leading to new types of understanding. If the format of the classroom is widely varied, every student can develop their own method of learning that plays to their particular strengths.

T&L 466 Learning Styles Assessment Project

For this assignment, I chose to take the Learning Styles Assessment test at the NC State University website. The test measured your results in four categories, each representing two "opposite" learning styles: Active or Reflective; Sensing or Intuitive; Visual or Verbal; and Sequential and Global. My results for each of these categories was as follows:

  ACT                  X                                REF

       11  9   7   5   3   1   1   3   5   7   9   11

                          <-- -->

  SEN                                      X            INT

       11  9   7   5   3   1   1   3   5   7   9   11

                          <-- -->

  VIS                                      X            VRB

       11  9   7   5   3   1   1   3   5   7   9   11

                          <-- -->

  SEQ                  X                                GLO

       11  9   7   5   3   1   1   3   5   7   9   11

From these results, we can infer that I am: slightly more Active than Reflective (1-3 is considered a "normal" range); more strongly Intuitive than Sensing; far more Verbal than Visual; and slightly more Sequential than Global.

To me, these results make a lot of sense: I've always had a hard time forcing myself to read textbooks (although I excel at reading when it's recreational), and consistently get more out of in-class discussions and lectures than I do assigned readings. I also tend to rely more on my own instincts when it comes to situations where I don't have all of the facts, so my being more strongly intuitive does not surprise me.

If I were faced with a class with similar learning styles to my own, I would very likely rely almost exclusively on in-class discussion and lecture to disseminate information, and try to give students a better sense of the philosophies and reasoning behind what I am teaching them. However, since it is far more likely that I will have a more even spread across these styles, I would be more likely to create my lesson plans in a way that would engage the greatest number of styles at the same time: ideally, we would have hand-outs about all of our discussions, have plenty of time for working through problems as a group and individually, and have an even balance of facts and worldviews.