Introduction

Let's start with me. My name is Rebecca, which you can see on the side. I guess this whole process really started when I was tiny (about to begin or already in Kindergarten) and my first grade teacher of a mother had me with her at school and we were working on pulling pages out of first grade math work books and sorting them. I'm not exactly sure how or if I was helping (being the mother of a 4 year old right now, I'm sure I wasn't), but my mom decided to start asking me the questions out of the books. According to her, I was able to answer them all, or at least most of them throughout the book. I'm not saying that I'm a genius, but clearly I had a knack for math.

As I grew, I had varying amounts of confidence in this knack. I remember being in third grade and being very upset at myself and thinking I wasn't any good at math because I had one particular friend who finished her assignments before I did. It didn't matter to me at the time that I had higher grades, she finished first, so she was better. Then in fourth grade we started the dreaded timed multiplication tests. Given my third grade history, you can probably see that this was a bit of a sore point with me. I was in the high math group, but I was not fast enough with my timed tests, so I was (apparently, according to my mother who would remember much better than I would) terrified that I was going to fail the entire grade.

Then came middle school. At the end of sixth grade, the class was given a placement test, and I guess the top third got to be in Pre-Algebra for seventh grade (I'm sure there was some cut off score, but it was rather convenient that out of about 70 kids, about 20 were in the advanced class).  Life was good, everything made sense, and then my teacher went on maternity leave. I was still doing alright, but none of my friends seemed to understand, so I got to help my friends, and for the first time, I noticed how a good teacher can really change how a student learns math. I made a very 12 year old decision to become a middle school math teacher.

Then life happened, my mom got a new job in a new town as a middle school Lit teacher, I got to hear all sorts of wonderful stories about those seventh graders, I stopped growing at a respectable but petite-ish 5'5", and I fell in love with Calculus because of an amazing teacher who worked extremely hard to work his four cats into every chapter of both Pre-Calc and Calc 1.

I went to college and knew that if I was going to teach math, I would want to teach Calc and the more advanced math, and I had issues with trying to be an authority figure to students who were five years younger than me and possibly 6+ inches taller. Thanks to all the middle school stories, I jumped from majoring in Secondary Math all the way to Elementary Ed at the University of Missouri- St Louis, despite many wise words from my Dean and my Elementary Math Methods teacher.

I pushed through my Elem Ed program in three years for personal reasons, only to find out that the semester I was doing my student teaching, the school was adding a minor in K-6 Math, so I missed out on that.

I graduated, got married, moved to New York state, subbed and then got a job teaching third grade at a private school. I taught for three years in a single section school with classes ranging from 24 to 10. All the time, I was working on classroom management, behavior management, building rapport with parents, finding a ELA and Social Studies approach I could believe in and teach to third graders, so I (unhappily) just went ahead and taught math from the Saxon scripts.

Then I was able to move to the position of 6-8th Math and Science teacher at this same school. I was thrilled to be able to focus on what I really loved, including starting an advanced program for the 7th and 8th graders which included Algebra 1. Unfortunately I found that most of the students had a very weak foundation in operations and skills, many of the 7th graders almost literally did not remember how to do long division. This was also at a time when the school was shifting to Common Core and changing expectations for all students, moving them to a level of math, they were mostly not prepared for.

During this time, I also began working on my MEd in Curriculum and Instruction for grades 4-9, with and emphasis in STEM. I thought this would give me that additional skills and concepts I needed to really help these (and future) students.

Life often has other plans, and after one year in middle school, focusing on math, my family moved because of my husband's temporary job transfer.

While my husband worked, I completed my MEd and began a simple pre-school program with our then 3 year old daughter. We have now moved back to New York State and I am continuing to homeschool, along with my neighbors who have a 4 year old and a 6 year old. We are implementing a Classical approach, which alleviates many of the curriculum issues I saw when teaching third grade.

However, math has, in my opinion, been overlooked. Other than an emphasis on learning facts, Classical schooling follows regular math practices, including recommendations to use the same Saxon lessons I used before.

Now Saxon is a fine math curriculum. I does a good job of achieving it's goals and there are many areas in which it excels, but I still have reservations with it.

As you saw, I don't really have any formal math education myself past Calc I, though I did have an introduction to Logic in another course. But there are many things that are accepted practice in math curriculum, almost the world over, or at least certainly in the United States that I have issue with.

1. Telling time, measuring to the nearest anything, recognizing coins, counting coins, knowing how many cups in a gallon- These concepts are not math. They are good life skills, or have a wonderful home in science, but the concepts in and of themselves are not math. They can be used as excellent tools to teach math, most notably skip counting, which serve as a great K-3 introduction to multiplication tables, but just because a concept uses numbers does not mean it is math.
2. Fractions- They are taught too early and used with non-math concepts (see above). While I was in my Math Methods class back in undergrad, we had a guest teacher come in and walk us through his revolutionary method for working with 3rd-5th graders and fractions. His first question was "Why do we teach fractions?" Many answers were given "To help with baking, to tell time, to manipulate measurements".  Our guest speaker renounced these ideas, just like the students in classrooms do when teacher tell them these reasons. Finally, after critical thought to a time when something isn't labeled "1/4 cup", I came up with the answer, to solve equations in Algebra and beyond. The teacher seemed rather surprised and relieved to tell me this was correct (I guess that's not a connection most elementary teachers make). So what that means is that in first or second grade we start students working on a concept that they won't really need until 7th or 8th grade. That means 5-6 years of vague problems and procedures because students are being forced to artificially create problems.
3. Fractions with respect to Division- Fractions involve taking a single thing and breaking it up in equal pieces. Division involves taking multiple things and breaking them into equal groups. Which do you think would be easier for a small child to understand, splitting a group or breaking an item? Fractions are introduced in late first or early second grade, division isn't introduced until late third grade or early fourth.
4. Integers- Again it's a timing issue. Again we have an abstract concept that won't have any real meaning until pre-Algebra and beyond being taught to 7 and 8 year olds while being shackled to concepts such as basements in hotels and winter temperatures, all because curriculum writers at some point in history decided that if students were introduced to it later they would not have sufficient practice to master it when needed (I assume that is the reason, I have nothing to back me up here. I assume that is also why fractions are taught so early). I have this crazy idea that when math is taught with, or at least nearer to it's appropriate context, students understand it much better and more easily.
5. Context- I know I'm insane. I hate probability, mostly because anytime it comes up in a book there is that stupid question about making pairs of socks in the dark. Students know BS when they have to deal with it. Math is taught in such isolated ways that many students don't understand how or when to really use it, and others just get fed up with the BS, leaving a (I feel) small percentage hanging on to go into math related fields.

So now that you know more about my math history than you ever wanted, and think that I am a raving lunatic for my ranting, here is my proposal. I want to create a new curriculum that addresses these issues that I see in, let's call it pre-college math. I'm sure I will have many more issues as I go, but I want to help fix some of these problems, especially for my daughter.

I am fortunate to be at a place in my life where I have the time to work on this kind of a project, and the motivation. I was working with my daughter and her school mate on a math lesson -writing the numerals for 19-26 and I asked myself "Why can't they be starting on place value now? What's stopping them from learning to see those groups of ten?"

I want to use this blog to record my thoughts on books and article that I read, any classes I take, and hopefully get feedback on materials I make for my daughter (and I hope other students as well).  I don't know how frequently I will be posting, but hopefully this will be a good record and lead to some useful things for students elsewhere, and since I am annoyed with the commercialization of education these days, I am going to do my best to read books from the library or other things I can get for free, and then post any materials for free for any kind of use. I can't guarantee professional looking worksheets or lesson plans, but sometimes free is better than pretty when you're a teacher looking for a lesson at midnight or during your prep period.

The one thing I has really missed about working in a real school is the opportunity to talk to others about educational ideas, philosophies and approaches. Please leave comments, questions, or advice. If we can make this a community it will help everyone!