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As an additional note, the Home School Resource Center will be hosting a sign up day on Tuesday, July 30th from 3:00 to 4:30 pm and from 6:30 to 8:00 pm. Mr. Freitag will be on hand to answer questions about the appropriate math class for your student. More information can be found at hsresourcecenter.com.
Welcome! How did you get started working with homeschoolers?
Soon after we were married, my wife and I had gotten involved in teaching Sunday School in our church. I enjoyed the interaction with the students and some folks thought I had a good sense of how to teach. As my own children were being homeschooled my wife did the majority of the teaching. When the children progressed in grade level and the workload increased for everyone, I increasingly spent time with them on math and science questions. I found out an important truth: you find out if you really know something when you can help someone else “get it.” I found I had to work at figuring out how to explain things to young students in a way that they could grasp. It was a challenge I found rewarding for both me and my children. So much so that in 1998 when the Home School Resource Center opened I quit my day job and signed on. It was big step of faith
What is your favorite thing about teaching homeschoolers?
All students are different and have different ways they learn. But one trait all students ought to have in common is curiosity. I love it when students ask questions that can’t be answered with a simple yes or no. When the class can get past just wanting to know “did I get the right answer?” I know we’re making progress. Adding logical thought processes and a bit of analysis to curiosity can make for a strong foundation for doing well in math and science. Seeing students get over the “I hate math” syndrome (where does that come from anyway?) to “what happens when . . . ?” is my favorite thing.
You have been teaching home schooled students for over fifteen years, how has homeschooling changed in that time?
Lots! Students have access to more information and demonstrations and how-to articles and courses on-line than ever before. So, for most students there is little excuse for not being able to find out things about the subject they are studying or find tutorials on any math problem. The issue is still one of learning how to study. That hasn’t changed, and probably never will. Sometimes I think homeschool parents think that since technology makes everything so much easier to access, in vibrant colors, with all the latest toys, that their child can’t help but make better grades. They still need to learn to read and study for understanding as well as content. They still need to know that life is a continuous series of “word problems” that need to be worked through with care using sound reasoning skills.
How important is a solid foundation in math? Can you give us an idea of some of the basics you like your students to know before they begin Pre-Algebra?
Math is the language of science. All technology (the “stuff” we use every day) is applied science. Every interaction one has with the natural world or the physical world or society requires application of known facts and reasoning skills. Math supplies the students with the “toolbox” of skills to succeed in all of those various interactions.
At the Pre-Algebra level, a student is really demonstrating whether he / she has a good toolbox of skills and concepts to make additions to. 1) arithmetic (adding, subtracting, multiplying, and dividing whole numbers, the number line), 2) fractions (the basic concept plus their relation to percents and decimals), 3) factors and multiples of composite numbers, 4) number theory (prime numbers, patterns, and sequences), and 5) geometry (basic ideas such as polygon shapes and names, area and volume).
The Resource Center has added classes for younger math students this year. Why?
I have seen an increase in the last five years or so in the number of students who are not ready for Pre-Algebra (see #4 above). The basic understanding of math as a language is not there. At the same time, there is a lack of understanding what the student is trying to do with any given problem. As one student put it, “Show me how to do one problem and I can do any like it.” Higher levels of math (and the rest of life!) are never like that. The student has to have an orderly, usable, and ready toolbox with a recognition of what skill or concept is to be used. To extend my analogy, a mechanic must know whether the problem is electrical or mechanical, and then he must know whether to use a wrench or a screwdriver to probe deeper, run more tests, or repair a part. Math is the toolbox to solve science and technology problems. It continually builds upon itself. A good foundation (toolbox) is absolutely essential.
There is also a nationwide push to require a core curriculum of math concepts at every grade level. One result of this is that some subjects that used to be Algebra 1 are now required learning in Pre-Algebra, and Algebra 2 concepts moved down to Algebra 1, and so forth. Geometry concepts are added in at appropriate levels as well (even though Geometry as a separate course is still required). The core standards follow what is known as STEM education (Science, Technology, Engineering, and Mathematics). The goal is to get more students interested in math and science related careers. The practical benefit for all students is that it is a tool to help them learn to make sense of the given problem, determine what mathematical model fits best, and calculate viable solutions. Or, the way I like to put it, “What do you know? What do you need to know? What do you do?”
I know parents often feel like they need to keep their student moving up to the next level each year so they have enough high school credits, but at the same time the student isn't always ready for the next level at the beginning of the school year. If I had to choose between repeating a math class and moving to the next level, which would you recommend?
Well, my dad used to say, “You find out what you learned in the last level when you get to the next level.” But sometimes a parent or teacher can tell that their student has not captured the basic concepts in the last level. Knowing how much harder it is going to get for a student who is weak in certain areas of math at the elementary or Pre-Algebra level, I would suggest either re-testing or remedial work. This is a parental decision, of course, but some things to think about are: What are my child’s bents and aspirations (not everyone needs straight A’s in math)? What is my hurry? What difference will it make if my child starts high school a year later than we originally thought? What other courses at the high school level will be adversely affected by a weak math background? Is the issue lack of effort or lack of understanding? Is there some way to help my child see that math is a tool or skill to be learned in order to do something else. Learning to add and multiply fractions is an exercise to be practiced just as learning to dribble and pass a soccer ball is a step in learning to play the game of soccer.
How can I prepare my students so that they feel confident on the math sections of the SAT and ACT?
The academicians who devised the textbooks that I teach from say it this way, “The Standards for Mathematical Practice in the Common Core . . . stress the importance of strong problem solving and reasoning abilities to develop mathematical proficiency.” So, first of all it involves practice – what I call “the grunt work.” You just have to do it. But, it is also involves practicing the right things. In the case of the Standardized Testing problems it is practice in recognizing a) what kind of problem is being presented (what do you know?), b) knowing what mathematical models fit the problem (what do you need?), and c) seeing what mathematical manipulations are required to reach a logical solution (what do you do?). Then do some more of a different type . . .
If you could give every homeschool parent one piece of advice what would it be?
Instead of putting it as “advice” let me raise a question that could be put to the student. When I was growing up I would be asked by adult friends of my parents or by my grandparents, “What do you want to be when you grow up?” I think a better question is, “How do you want to be when you grow up?” Do you want to be successful in business, or in raising your children, or in being able to explain why you believe what you believe? Are you always wanting to learn new things? Do the changes in our world frighten you? Excite you? Cause you to ponder outcomes or consequences? Critical thinking and reasoning skills are a requirement in any career, home, church, and community. Don’t partition off mathematics or science or history or language skills or art or geography from one another as subjects to be checked off on a list. They are meant to be thoroughly integrated, wrestled with, curiously probed, related, and enjoyed.
1 comments:
I really enjoyed the Geometry course I took with Mr. Freitag in my junior year - apart from the chapters in the Jacobs book dealing with three-dimensional figures, but that was only because I have a wretched time envisioning them. The instruction in proofs and Such Like was, for a geometry class, surprisingly painless. His tutoring my Physics course was also very helpful, as there were parts of the book that left me absolutely baffled and in need of someone to restate and explain the case. (It shouldn't be this hard to wrap one's mind around the principles of acceleration!)
Thank you for the interview!
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