Welcome

I am a licensed and experienced math teacher and tutor. I have more than 15 years experience tutoring and more than 10 years experience teaching. I have both an undergraduate and a graduate degree in Mathematics Education. I love teaching math and working with students. It's an incredibly rewarding experience to work on hard problems and to really understand why something is working.

I offer a few tutoring services to choose from in the Portland metro area. Please let me know what works best for your family.

Saturday, February 25, 2017

How I Teach

I am a "constructivist" teacher because I am a "constructivist" learner. I always needed to know why something worked. If I didn't understand, chances are I would soon forget how to do it. Memorizing is a temporary ineffective solution when the true goal is learning. It might get me through a spelling test but it is no way to learn math. Tricks and over reliance on memorization is my main critique of traditional math education. You might see quick gains but those gains are temporary and not gains that can be built upon.
When you instead construct your understanding from previous knowledge that new understanding is lasting. It also is easily transferable to other topics. Math is beautifully setup to allow for this construction. It is also far more enjoyable to learn and teach in this way.
I also naturally look for applications to what I'm learning or teaching. Being able to apply new information helps with authentic incentives. Students want to know why they are learning something for a good reason. "When am I ever going to use this?"  is a valid question.

Saturday, February 11, 2017

The Problem with Algorithms

What is an Algorithm Jess? 
It's basically a set of rules to be followed to perform a calculation. They are great for computers. They are easily performed and consistently give the correct answer.

What's Wrong with Teaching Algorithms?
Basically, students are not computers. Any parent can confirm that children are not designed to take inputs and generate consistent outputs. People make mistakes, they have deeper thoughts, they interpret findings, they think "what if this was different," they forget and they get bored.

By teaching algorithms we are teaching only how to get the answer. We are not teaching how math works and the structure/logic supporting the process. When we treat student like computers, we forget that interpretation is hugely important. We also do not allow for the student to understand how the answer came into being. At best, a student has a surface understanding of what just occurred. They view math as a series of boring rules to be memorized and not as the beautiful logical structure that it is. When you approach math as being a series of interconnected topics student can fill in missing pieces with a little problem solving. They can construct there own understanding and continue to build on that understanding. We can given them those tools that allow for independence in math but not if we keep teaching tricks and have them memorize rules.

Examples of Algorithmic Teaching
  • Cross Multiplication: every time students see two fractions, whether there's a equals sign in between or not they want to cross multiply. Instead we should be teaching inverse operations and solving equations.
  • The Triangle Trick: This is a new one for me that I was introduced to by a science teacher. Apparently, we are unable to teach how to solve one step equations in science classes. So F=MA, is just too difficult to work with if I asked a student to solve for the mass.  So they teach students how to put this equation into a triangle that somehow makes it easier to understand. Here I thought dividing on both sides was straightforward enough. 
  • The Distance Formula: Why memorize yet another formula when the Pythagorean Theorem will suffice? 
  • Long Division: There's a few other methods that reinforce what your actually doing when you divide.
  • Almost any Volume Formula: If you know what volume is and you can find the area of a triangle and circle your pretty well set.
  • The Quadratic Formula: I taught my student how to complete the square and then proved the quadratic formula using that method. Then we timed students doing both methods. Completing the square usually won. I do really enjoy the Quadratics Formula song, so I will continue to teach it. 
I could go on and on. When I look back at when I've enjoyed learning or teaching I was not memorizing or practicing a process. When I've enjoyed math the most I've been figuring something out, asking a question I don't know the answer to, extending a topic and going down the occasional wrong path.