B. Educational Beliefs and Practices Reflection

 B.1 Why Teaching is Important to Me

Teaching is important to me because I find joy in helping others come to grasp what I know and understand. I can see patterns and I can explain them in simple terms. I understand how numbers work together and I can help others recognize numerical relationships. Many people have told me that I explain things so clearly that they finally understand after having talked to me. Teaching is important to me because it is the vehicle by which I can use my talents to help others learn and grow. Education is critical to have a well functioning country and community. Education, in my opinion, is the key to conquering poverty and ensuring personal and familial success.

B.2 My Beliefs About Teaching and Learning

At my most recent job interview, the math department chair asked me if anyone could learn math. I said, “Yes, as long as they want to.” Thanks in part to my answer I was given two classes that have a high number of students with IEPs. Regarding learning, I believe that any student that wants to learn math can learn and show growth. Students enter my class performing at a range of mathematical abilities. Regardless of the level of understanding, if a student wants to learn, then he will be able to learn. I will provide the tools, instruction, guidance, and practice that he needs in order to progress. With his continued desire to learn, the student will show growth in mathematics.  Of course, this will go the other way. If a student does not want to learn, he will not learn. Mary Davenport writes about how to help students be motivated, and that “anytime students are unmotivated, forget about it.” (Davenport, 2022). Davenport lists Autonomy, Mastery, and Purpose, as key factors in helping “boost high school students’ sense of agency and motivation.” (Davenport, 2022). 

In regards to teaching, I believe it is my duty as a teacher to provide the tools, instruction, and practice required for students to grow in their mathematical abilities. I will teach and explain to the best of my ability. I will guide students to figuring out problems and coach them until they have mastered lesson objectives. Ben Johnson explains, “Students learn best by doing, and active teaching encourages active learning. Teachers should treat students as active participants in the learning process…” (Johnson, 2015.) When I speak, students do not always internalize math concepts. They figure things out by doing. As they try to solve problems, they will discover and begin to see the patterns. Being a coach and guiding students through problems is my favorite effective way of helping students learn math.

B.3(a) Fostering Problem-Solving Skills 

I want to foster problem-solving skills in my students. One of the instructional strategies I use to build students’ problem solving skills is that I elicit how to solve a problem in multiple ways. Just because you are punching numbers into the calculator doesn’t mean you are going to arrive at  a feasible solution. Your calculation may be correct or incorrect, or may not make sense in the given context. Having students discuss and come up with more than one way to solve a problem will help them to solve problems with varied approaches. A good thing about having 30 students in a classroom is that there is bound to be someone that has solved the problem in another way. Solving problems in more than one way will help students build mathematical understanding and the ability to correctly solve future problems. 

Another strategy that I use to develop problem-solving skills in my students is to use relevant real-life examples. When a student can relate to a problem, he can visualize himself in the situation and will exert himself in the problem solving process. For example, if I ask a young person at my school how much a giant bin of alpaca furs will cost, he may have no idea what an alpaca is. The problem is already irrelevant and solving it would be meaningless. However, if I asked a more relevant question such as, “Is it a better deal to pay $10 for a small 10 inch pizza or $20 for a 20 inch pizza?” The student may already have an idea since he has paid for pizza before. He also may remember the last time he ate pizza, his favorite pizza place, and probably remembers eating pizza with his family or friends. The problem is immediately relevant and more intriguing than that alpaca fur problem. Using relevant real-life examples helps students be interested, engaged, and motivated to trudge through and develop their problem-solving skills.  

B.3(b) Measuring Student Mastery of Problem Solving

I will create an assessment that will require students to explain two different ways of solving the pizza problem. If they are able to approach the problem in two different ways, then they have demonstrated student mastery of problem-solving skills. If students are able to come up with the same answer using both strategies, then they have skillfully solved the problem and checked their answer as well. For example, a student might draw pictures of two pizzas, one with double the diameter of the other. He could easily draw two small pizzas inside the large pizza. He will be able to deduce that while the price doubles, the large pizza has more than doubled in size. The large pizza is therefore the better deal.  Another strategy would be to calculate the area of each pizza using a calculated radius. Then we could find a ratio of price per square inch of pizza. 

I will create a formative assessment in-class assignment where I give an answer and ask students to come up with the problem. This is another effective way to approach a problem - often called “reverse engineering.” If students are able to come up with a story problem that results in the answer that I gave, they will have demonstrated student mastery of creative problem-solving skills. Ideally students will use the skills we have learned recently in class to come up with their scenario. (Yet, in a class of 30 students, there will likely be someone who comes up with an unrelated story problem.) For example, I may say, “The tree is 25 feet tall, please come up with a story problem using trig that will result in this answer.” Students may respond, “The shadow on the ground is 25 feet long and the sun is at 45 degrees from the horizontal. What is the height of the tree?” Using tan 25 = opposite / adjacent, students can calculate that the tree will be 25 feets. Of course, there will be a clever student that will realize this hypothetical triangle is an isosceles and doesn’t need the tangent value to figure out that the tree is 25 feet. 

B.4 Building Positive Relationships with Stakeholders

It is imperative to build positive relationships with school stakeholders because educating young people is a united effort by many parties. Parents are key stakeholders and it is critical that I work with them to ensure the best possible education for my students. Parents can make or break a student’s success in my class. As such, I communicate often with parents. I purposefully send a progress report email to all parents after every unit test. After students have taken the unit test and grades are finalized, I send an email to all parents with an updated grade sheet for each student. Happily, our district’s tool, Skyward, has this built in capability. It is important to me that parents are up-to-date on their student’s performance in math and never surprised at the end of a quarter. Thanks to these emails, I’ve seen parents get involved to improve student performance and ask relevant class questions. I will timely and professionally respond to any inquiries made by stakeholders. If parents email me, I will be sure to answer their questions quickly and politely. Occasionally I have had upset or confused parents email me, and by being timely and professional, their concerns are assuaged and we forge good working relationships. 

References

Davenport, Mary. (August 24, 2022). “Boosting High School Students’ Sense of Agency and Motivation.” edutopia.org. Retrieved from https://www.edutopia.org/article/boosting-high-school-students-sense-agency-and-motivation

Johnson, Ben. (July 17, 2015). “What is Your Education Philosophy?” edutopia.org. Retrieved from: https://www.edutopia.org/blog/what-your-educational-philosophy-ben-johnson