“The most important years for developing a solid foundation upon which to build lifelong learning. We have one core belief: that the most important time period in a child's education is Pre-K to 4th - 5th grade. We believe that's when the educational foundation is developed and enables future.” (At Home Tutor, LLC)
I have told parents that if their children come out of elementary school knowing their times table forwards and backwards it will serve them well to learn any topics they miss along the way (fractions, decimals, percents). I know the times tables seem like a simple “rote” exercise but it is more than that. Take a 10 by 10 “times table” chart and think about all the relationships between columns and rows and even diagonals. Have them think about the connection of addition and subtraction to multiplication.
Starting earlier than even multiplication tables, just understanding the relationships of numbers will serve them very well. I kept a wall chart of just the numbers from 1 to 100 in rows of tens on the wall next to my son’s bed from his earliest years. By the time he was in kindergarten, he was doing mental math calculations.
With an intuitive understanding of the basics, students will be able to catapult themselves into future educational situations in just about any subject, IF they are solid math students by the end of 4th grade. Add a solid reading background and students will be able to learn on their own as well as with an instructor. And isn’t life-long learning the goal?
Another method that I used with my own children was throwing multiplication facts at them when we waited for a train to pass or if we were waiting to be served in a restaurant or any other place where we had to wait – I would just throw out quick practice questions (such as 4x6, 9x3) just random numbers from the multiplication table. They seemed to enjoy it and when they were together they giggled about who was faster.
OK – I know at this point, you’re thinking “But we have calculators!” Yes, true, and let’s save those calculators for more advanced math situations where the learning is about theoretical concepts and we don’t want to get bogged down by numbers. I had a college professor who filled up three blackboards with an advanced theoretical concept and a student raised his hand to correct a numerical error early on in the process. This noble laureate (Linus Pauling) responded, “Oh, numbers, they are just place holders.” He was teaching a concept, that’s what his teaching was all about. And then there’s the famous quote “Numbers are to mathematics as spelling is to writing.” But, this is no excuse for not learning basic arithmetic or learning how to spell. But, please, do show leniency about calculations and spelling when bigger concepts are being taught. In my high school math classes, I always gave partial credit to a student who worked the steps correctly but messed up a calculation along the way. Calculators do have their place at the right time. And when assessing a student’s writing, A/F means they said it well but their spelling and grammar was not great. Conversely, F/A means they were great in spelling and grammar but their content was not great.
During my tutoring years, a 57-year old mother of one of my students revealed to me (through her tears) that all her life she felt deficient not knowing basic arithmetic. It was her secret burden. And, now, she was trying to get into culinary school and the entrance exam had basic arithmetic questions. She was paralyzed with fear. Why? Because she never mastered basic multiplication and had relied on her calculator for every little calculation. She had no clue how to do fractions. I worked with her for a few sessions and she gleefully called to tell me she passed the entrance exam and got into culinary school. It’s sad that she had to live so much of her life with her self-esteem fractured by not knowing basic elementary math.
As a high school math teacher, I vividly recall the Junior Algebra student who raised his hand during a lecture and asked “What is 1/4 plus 1/2?" I tried not to let my mouth drop open and simply explained his question. Other students may very well have stumbled on that same issue but may have been afraid to ask. Therefore, even material that students should know from previous courses years ago but, either forgot or never knew, it’s important to fill in those blanks just to keep them on “the path” regardless if it adds a couple minutes to the presentation. This is another example how those early years of math education affect the future…
And then there’s the issue that girls who are ahead of the boys at the 4th grade level are generally behind the boys from that point on. This adds to the STEM gender gap. Is it genetic? Is it environmental? Is it societal? A good article with lots of data on “Gender Disparities” at the Illinois Math and Science Academy is located at https://sites.imsa.edu/acronym/2017/12/15/get-schooled-gender-disparities-in-imsa-academics/ . Another interesting article pointing out the discrepancy between female and male achievement is located at https://nypost.com/2019/04/24/girls-do-worse-in-math-and-science-classes-with-high-achieving-boys-study/
Who am I? In addition to many years as a high school classroom math teacher in three states and creating these 45 learning modules for K-College math and reading, I also spent a couple decades tutoring one-on-one where I could really analyze my students’ learning styles.
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