Assignment 3: Unit plan

EDCP 342 Assign 3: Unit Plan- Michelle Li

Wagner & Herbel-Eisenmann on math textbooks

    I am surprised at the implications made by the author about how language affects students' positions in relation to mathematics.  The articles states that the absences of first person pronouns affects nature of mathematical activity" and "also distances the author from the reader, setting up a formal relationship between them".  I can see how this can contribute to students having a hard time relating themselves to the math content, that may already seem so static and theoretical on paper, rather than dynamic and practical in the real world.  

    The author also suggest that the linguistic choices in textbooks affects students' positions in relation to their experiences of the world.  As one flips through a textbook from front to back, it assumes the reader is progressing with it, though, of course, this progression is different for every student.  The author poses an interesting question: "Would the reader think that his or her everyday experiences matter less than their mathematical experiences?".  

    I think textbook use in classrooms can be beneficial to both the teacher and students.  It can offer a different perspective and give students another way to approach mathematical concepts and problems.  However, I think teachers and students should be flexible in their thinking and teachers should not rely on the textbook content and progression as a sole guidance to drive the course content.

Sketches: Truncated Cube and Icosahedron

 

Dave Hewitt’s secondary school algebra teaching

    In the number line demonstration we watched in class, I liked the idea of adding sound and movement to show the numbers as they increased when moved to the right.  Dave Hewitt didn't write on the board, making it very simple, letting the students imagine the numbers through sound and movement.  I think it makes it more engaging, maybe because students are used to seeing math visually and statically on paper or on a projected presentation.  

    I like that the whole class was encouraged to say the answer as a group, instead of the teacher telling the students or the teacher asking one student.  I find that students are more willing to learn when it is from their own peers.  Perhaps hearing the voices of their classmates would help students remember information in a more meaningful way while connecting it to a group activity they did in class.

    I don't think Hewitt mentioned to the students what they were learning.  Hewitt simply presented a pattern to the students by showing them with a ruler and the wall.  Students slowly caught on and soon, the whole class understood without any explanation from the teacher.

    I can see myself incorporating all three points mentioned above in my classroom.  Math can get boring when it is practiced and learned in the same way, especially when students are stick in their seats for the whole period.  Learning math in various ways that use movement and sound can help attract students' attention.

Arbitrary and necessary

    Hewitt describes something as being arbitrary is was given through external sources such as teachers, books, the internet, etc.  To be learned, it must be memorized and when a person is challenged by the question "why?" to that arbitrary knowledge, they are stumped.  

    Necessary aspects of math are things that can be figured out on your own, unlike the arbitrary aspects.  Using prior knowledge, new information and concepts can be worked out to be true because of the process one goes through.

    I think it is problematic if students start seeing all math concepts and terms as arbitrary.  When students stop questioning and stop being curious about the "why", math becomes abstract and meaningless.  Students can't make personal connections to the material they are learning and this may negatively affect their understanding and interest.  I believe it is important to constant question students' thinking process when looking at math concepts and terms to encourage inquiry.  

FLOW in Math

    I experience a state of flow mostly through learning music.  I can sit with a new piece of music that is challenging, but enjoyable, working through the tough sections and I wouldn't notice that I spent a few hours sitting with my instrument.  However, this doesn't happen every time I play music, only when I feel like learning something new.  

    Recently in one of my math courses, we completed a high school math test.  Class time that usually went by very slowly, went by quickly because I enjoyed doing math that was familiar but evoked thought because I hadn't encountered it in a long time.  

    I believe a state of flow can be achieve in secondary math classes.  New information must be presented in a way that is approachable to students and that invites students to be creative in their thinking.  In other words, inquiry-based learning environments can be a good tool for this.  When all the answers are given or when full instructions or procedures of how to solve a problem are given, it does not encourage students to think further about the questions.  Using various activities and opportunities for group work can help with exposing students to new perspectives that they haven't seen before, therefore challenging students' thinking.