Eddie Woo tells his story of growing up struggling with mathematics, but changing his course of study in college from English/history education to math due to his realization of a need for teachers in that area. He came to appreciate mathematics in a way that he equates to how he came to appreciate music: it used to be a torturous chore that meant nothing, but became a beautiful and useful art to him as his understanding grew through experience. He calls mathematics a sense, specifically “our sense for patterns, relationships, and logical connections” (Woo). He discusses the idea of a fractal, which is a super cool type of geometry involving recursive patterns, and he shows how we see these shapes all around us in nature – in tree branches, human blood vessels, bolts of lightning, etc. He says that “all human beings are wired to see patterns” and that “we live in a patterned universe.” Through examples of how math is found in nature, Woo displays that math is immensely practical, beautiful, and more natural to us than we may have previously realized. 

While this TED Talk did not have the specific intention of sharing pedagogical strategies, Woo is a math teacher, and I can see how the concepts he discussed could be applied in a classroom setting to help students who struggle with a dislike/anxiety for math appreciate the subject. For example, to students learning about a new math subject that has the potential to be confusing (which is potential I believe any math subject has), showing them examples of where the concepts associated with this subject appear in the real world can help them care more about the subject. In a practical class, real world applications of problem solving can be shown explicitly. For example, in a pre-calculus class at my practicum, I witnessed the teacher giving the students an example problem that involved figuring out how much would need to be payed on a mortgage per month using an exponential equation. In a more abstract class, even if practical applications don't exist, it's often still possible to show examples of where similar patterns/logical structure appears in nature. Woo gave examples of this with fractals appearing in lightning bolts, river deltas, blood vessels, trees, etc. and also with "the golden ratio" showing up in flowers as the ideal angle of spacing between petals to create a beautifully patterned, symmetric flower where each petal receives the maximum amount of sunlight.

I can imagine adopting this strategy as a high school math teacher in similar ways as described above. Another really cool example is that, when teaching trigonometry, I can emphasize the applications it has in engineering and architectural work. I can remember when I was in my high school geometry class, I ended up talking to a friend of my father's who was an engineer working in construction; he told me that he uses sine, cosine, and tangent all the time. I was amazed that what we were learning in my high school math class was actually important in the real world. I want to give my future students that same awe for math.

Tarcia Lasha Hubert did a research project entitled "Learners of Mathematics: High School Students' Perspectives of Culturally Relevant Mathematics Pedagogy" to observe the effect of culturally relevant pedagogy (CRP) on students, particularly African American students. In order to achieve this goal, she taught a portion of a course meant to prepare students who needed extra help for an upcoming state math test using CRP.  Afterwards, five students, who were diverse in terms of ethnicity and improvement level, were interviewed to see how they felt about CRP as opposed to the type of pedagogy they typically experienced at school.

A key aspect of CRP is that it "helps students to maintain their cultural integrity by helping them realize that they can be themselves and still be successful academically. This is typically done by using aspects of students' culture in the learning process" (Hubert). One way that Hubert sought to do this was through the topics of the lessons she taught; she writes that these lessons were teaching the concepts of "quadratic and exponential functions," yet "the topics of the lessons included: (1) teen pregnancy... ; (2) perinatal HIV; (3) teen smoking; (4) football and soccer; and (5) saving money." She taught the mathematical concepts that the students needed to learn, but the themes that the problems were based on were topics that the students were familiar with. Not only did the students say themselves that these lessons were relatable and, therefore, more engaging to them, but their grades showed improvement from before to after these lessons. 

Hubert determines that there are six themes of CRP that she observed during this research project. Firstly, these classrooms are reminiscent of the students' home environments; for example, the lessons on teen pregnancy and smoking were relatable to what many students saw in their home life and with their friends. Secondly, a caring ethic is present in the classroom; the students feel wanted and as though their personal understanding of the material is possible and valued. Thirdly, plenty of opportunities exist for participation and collaborative work. Fourthly, technology, such as calculators and computers, is utilized; one student is quoted to have said “my calculator is truly my best friend now,” which inspired the image on this page. Finally, the students become both confident and motivated as a result of CRP. 

When I am a teacher, I plan to use these four CRP methods listed above to make my classroom a better place for my students. I can see how all of them are extremely important in a mathematics classroom in particular. I really see the value in making math problems relatable and interesting to students so that they will be able to be more engaged with the material, and I hope to always keep this in mind when making lesson plans; I'm grateful for the ideas of topics she used above. Fostering a caring ethic in my classroom is even more important to me; I never want my students to feel unwanted, undervalued, or incapable of succeeding at mathematics. It made me so sad to read in this research study that one kid admitted to having missed class in the past because he did not feel wanted there; I want to ensure none of my students ever have to feel like that. Creating opportunities for participation and collaborative work is something that I see the importance of, but I believe I have a lot to learn about what this looks like practically. Something that intimidates me about being a teacher is figuring out the balances between things like group work and individual work, letting kids volunteer freely and calling on them directly to ensure they understand, and making clear to them that I am happy to help while also letting them do some problem solving on their own. These are things I'd like to learn more about. 

Karli Bergquist gives an engaging TED Talk called "Finding math in the daily life of indigenous cultures" in which she elaborates on how we use math all the time in our lives. There are many students, and people in general, who claim that they are "not math people" or that "they hate math," but they make this claim without realizing that they use math everyday for activities that are necessary and even enjoyable. She points out that each of us did math today as we figured out how long it would take to drive to get where we are going or when we made ourselves a cup of coffee. Bergquist shares examples of her students coming to appreciate math through this new lens, seeing "math moments" all around them in things like a hummingbird beating its wings really fast. She also gives the example of her friend who claimed to not be good at math, but makes clothes, which requires designing, playing, locating, counting, measuring, and explaining. Bergquist says that whenever we do one of these actions, we are doing math -- we're just not used to seeing it like that. 

One teaching strategy that I am taking away from this TED Talk is making clear to my students that math is all around us, that it's important, and that it can be fun. I think it happens too often in schools that students grow to "hate" mathematics because they had a bad experience where the teacher made math seem boring or irrelevant. I want to make it clear to my students that math can be relevant and enjoyable to them, and I think I will try to do this in a similar manner to how Bergquist does: by letting them appreciate the math around them that is relevant to them as opposed to just sticking to the curriculum, textbook, or lesson plan with no flexibility allowed. 

In this TED Talk, Dan Meyer discusses the issue that math is being taught in such a way in American schools that the students do not retain the skills they should, namely "the application of math processes to the world around us." He suggests the fascinating idea that our culture's practice of doing things like watching sitcoms with problems that are resolved within a short period of time make it harder for us to work out real world problems that take more time and effort to solve. He uses the key phrase "patient problem solving" to describe how we need to be teaching math. 

Meyer goes through a word problem from a math textbook and explains how the material could be presented in a better way. One significant quote from him is "the math serves the conversation; the conversation doesn't serve the math." What he's getting at is that we use mathematical skills because they help us solve the problems we are interested in solving; it doesn't make any sense just to plug numbers into formulas and to follow the correct steps to get to an answer just for the sake of doing math, and no one is going to retain math that is taught this way. Instead of throwing a problem with step by step instructions at his students, he shows how he introduces the visual and the question about it and asks what they think the right answer is. Then, they slowly move through the process of getting to the answer using the correct processes and the correct pieces of information, but they get to see and understand for themselves why each step and piece of information is necessary. 

He notes that man students come to him suffering from the following "viruses:" lack of initiative, perseverance, and retention; an aversion to word problems, and an eagerness for the formula. However, he also says that the strategies discussed in this TED Talk have helped his students improve in this areas over the course of the school year. 

Meyer offers five specific strategies to teachers: "use multimedia," "encourage student intuition," "ask the shortest question you can," "let students build the problem," and "be less helpful." I plan to try to incorporate these strategies, which are built around the goal of helping students learn how to think, when I am a teacher. I do think I need to be careful with the "be less helpful" piece of advice because, of course, I want my students to feel like they can ask for help; I will just need to find the balance between being helpful and letting them figure out what they can on their own.