Over the last year I have have the pleasure of working with Dr. Gregory of Dr. Gregory & Associates at an elementary school where we both do some consultancy work. He is constantly talking about the "40 Year Effect" that our instruction has on our students. Dr. Gregory advocates that teachers should plan instruction experiences that stay with learners for 40 year, not 40 days or 40 months. Listen to the podcast below to find out more about the "40 Year Effect" and how you can achieve it.

I mention the 40 year effect, because I have been working with some adults who are looking to get into the renewable energies field, but did not meet the requirements in a certificate program. In order to gain the skills needed to meet the requirements they had to take part in a 5-week Math Boot Camp and I was their instructor. Initially, I was told that the concepts that I would be required to teach would be high school level mathematics, but in reality the mathematics concepts I actually had to teach would normally be introduced and taught between grades 3 to 7. Topics such as area, perimeter and volume, operations with fractions, using measurement tools, decimals and percents, and ratios and proportions. Much of my experience mirrored what I see at the K - 12 level.

**As a teacher:**

- I did not feel that I had to time to adequately prepare. The opportunity to work with these students came along rather suddenly and I had 2 days to plan out the 5-weeks.
- I did not have access to any assessment data until after I met my students. When I the opportunity came up for me to see the assessment data we began to realize that the assessment and the online tool for assembling the assessment data were inadequate.
- I was given a "curriculum" and asked to teach it. The "curriculum" consisted of 100 PowerPoint slides broken down by topics to teach each week. Upon review of the first 10 slides, I found 3 mathematical error or imprecise use of mathematical language.
- The "curriculum" did not math the assessment tools. I realize rather quickly that in order for students to "progress" in the Math Boot Camp they had to make gains in the online assessment tool. However, the online assessment tool did not match the flow of the "curriculum". For example, If a student tested in at Level 5, then they would begin the Math Boot Camp focused on ratios and proportions, but the "curriculum" did not address that topic until week 4.
- I was not told that my students would have a final exam until 4 before the last class. The director decided that the students needed to take a final exam that was separate from the online assessments that they had been taking. I saw the final exam 2 days before the last class.

**My students:**

- Reflected a very wide range of mathematical understandings. This group had people from all walks of life...a nurse, a lawyer, a carpenter, a recent high school graduate, a computer programmer, a handyman, a solider in the U.S. Army, etc. Most of my students were math phobic. Most of my students did not like to communicate their understanding...they just wanted to get to the answer. Most of my students were very procedural in their reasoning. Most of my students could "see" and make sense of numbers when the ideas were related to money, but had great difficulty when the numbers were in a different context.
- Thought that I taught differently than anything they had ever experienced because I asked them to question, use more than one way to find a solution, work in groups, use mathematical sketches to visualize problems and used concrete materials to "show" and act out mathematical concepts. Most of my students lacked a deep conceptual understanding of the mathematics that they were being asked to use.

**The "40 Year Effect" via student comments:**

"Christine, I never knew what Pi meant. I never understood the relationship between the diameter and the circumference. I never understood that the circumference was the perimeter of a circle. Thanks to the (hands-on) activity that we did...now I will never forget."

"Christine, I can see the benefit of understanding now and not just knowing a procedure. I was trying to explain how to do something to another students, but realized that I did not understand enough or another way to explain things and they could not get it my way. I only knew how to get the answer my way, but I did not really understand what I was doing."

"Thanks for teaching us so many ways to solve one problem. I understand now and I have options. I now solve one way and check with another way and I know that I am correct. My teachers in school only taught me one way and if I did not get it, then I was stuck."

"When my son was in the 3rd grade he tested off the charts and was placed into a talented and gifted program. But where I come from, 'talented and gifted' programs are just codes for 'CEO training' programs. My son is brilliant and a little quirky, but in this 'talented and gifted' program they killed his creativity. He had to find solutions to way that they showed him or he was wrong. He now hates math is is very phobic about it. He doubts his abilities and his intelligence."

"Christine you taught me how to measure. I never knew. I thought that I could not ever get it. I never knew that it was so simple. It seemed so complicated before. I can measure now and I can teach my son."

"Christine, I had such a fear of math. I chose to become a social working, because I could avoid math. Now here I am trying to do better in life, change careers and it is the math that is hold me back, but at least now I know that I can do it."

"I did not like to explaining part of the class. I can get the answer, but Christine insisted that we explain things."

"You told us to sketch it out. I would not have gotten this one wrong if I drew it out. OMG, I can believe I left out the calculations for the area of the second window. I just did 1 window and the area of the wall."

"I knew that I was going to fail the final, but I was courageous and came anyway. I tried. I just need more time to get this stuff. Thanks for helping me get this far. The online tutoring sites (NutShell Math via Cosmeo, Khan Academy) that we were using...are they going to be available even after the class is over?"

**What is your math "40 Year Effect" going to be?**