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.

EISNER: Three curricula all schools teach

     Eisner points out that values "are expressed in the kinds of illustrations that textbooks contain, in the language that is employed, and in emphasis that is given to the characters that constitute the stories that are read".  I find this interesting and I connect it to something I learned in psychology in terms of schemas.  Growing up, to me, curriculum meant the topics and content taught in classrooms.  New information is funneled into the minds of the students and that is the end of it.  However, in psychology class, I learned that there are two types of learning related to new information.  There is assimilation and accommodation.  New information either gets categorized into existing schema and possibly changes it or new schemas are created.

    The BC curriculum is split into different components that relate to each other.  The curriculum is based around the core competencies and describe the intellectual, personal, and social and emotional proficiencies students need for deeper learning.  Content is only one part of the curriculum and describes what students will know.  In any good learning environment, there will be more that just content learned.  Eisner's point about the values learned in schools can be seen in the big ideas that students will understand and the curriculum competencies that show what students will do and how they apply the skills learned. 

Battleground Schools Reflection

   I am surprised that the reading mentions that "there is no shame" in being "incapable of doing and understanding mathematics" and that it comes with positive social valuation.  The article mentions that during the progressivist reform, the reputation of math was that it taught students procedures to get to an answer but provided no explanation about the "why".  Therefore, many people thought of math to be useless in real life.

    John Dewey believe that there is a "split between knowing and doing, or abstract and applied knowledge".  He states that students "must engage in doing mathematics as part of a reflective inquiry" in order to become more knowledgeable.  This was during the early 1900s and I am surprised that the idea of inquiry and curiosity in mathematics for school mathematics was examined.  I feel that the current curriculum has only begun to incorporate more inquiry and project-based approaches in math classes.  Therefore, it has taken a long time to integrate these practices into classrooms. 

Oct. 21, 2021 Pro-d-day + Reflection

    After doing the TPI activity in our 342 class, I noticed that I did not see strong connections between mathematics and social issues.  I was glad to see presentations on social issues in the BCAMT conference.  

    The presentation I watched was "Challenged Accepted!  Use Project Based Learning To Explore Social Justice" by Carl Oliver.  Carl shared various activities that could be integrated into math classes and presented different frameworks that made sense to me once they were brought up.  

    The general outline of creating a project-based learning environment encompassing social justice is situation, exploration, and presentation.  I found it interesting that Carl shared Gutierrez's framework of rehumanizing math through connecting students to math by ways of history and culture.  It engages students and encourages them to think about themselves participating in making math in the real world.  Next is exploration by means of describing accurately a situation, making a prediction, designing something, or creating a product.  Lastly is presentation where students are given choice and autonomy to inquire and be creative.  

    I am surprised that these types of projects, that I have only seen arts, English, or social studies classes, can be so applicable in a math context.  I am excited to learn more about it and potentially use these ideas in my classroom.