Algebra for Kindergarten

This may shock [and perhaps outrage] some older folks, but concepts of algebra are now being taught in some schools throughout the U.S. Algebra Ugh! Lots of us groan at the word. I failed miserably in Algebra 1.  But is wasn’t my fault [said the student]. Yet, it really was not mine for a couple of reasons.  First, I had no pre-algebra in elementary school.  Second, I had a miserable ‘teacher’ in my freshman year in high school.  Third, I was severely right-brained at that time.  Algebra can be deadly for right-brained kids who use images to process things.  Do you recall many ‘images’ during your algebra classes?  All that I recall were black scratchings on white paper or beige scratchings on green boards.

Fortunately for many children today, they are given hands-on mathematical manipulatives to explore mathematics. Yes, explore rather than head-pounding or rote learning. All that I recall from my math arithmetic classes in grade school were paper, pencil and workbooks. Sadly, some kids today are taught exactly the same way which is why, sadly, so many adults have such poor mathematical concepts.

A number of year ago, I tutored women in math- women who attended GED classes in a woman’s center in an old church basement. Most had dropped out of high school because of pregnancy and/or financial difficulties. Their math sense could fit in a thimble. Their math skills were even less, yet they needed to pass the GED exam if they had any hope for independent living in society. Imagine the algebra requirement that stood before them. These women were not dumb, but they had had little preparation for high school algebra.  There were many reasons, but nonetheless, the fact was that they needed to solve algebraic problems to get their GED. Algebra was foreign to them; I may as well have been speaking Mandarin.

Take this simple equation for example:  2y = 10. “Why is there a letter in the middle of a math problem?” was the common question. Another more angry question might have been, “Why do we have to learn this s— anyway!” Luckily some of the other women would answer it, “Cause its on the GED test.” Some women dropped out and/or never came back. Regular attendance was an additional problem.  A few endured.

Yet, many kindergarten children [inner city and suburban] can easily solve this same algebraic equation.  How? Manipulatives like the one here.  Can YOU figure out how they do it?

EI-1070_LIf you said, “Put a blue marker on the right side ’10’ and then two blue markers on the left-side ‘5’ “then you are as good as a 5-year-old. And the teacher did not tell them to do that.  It was trial and error, or as the new math lingo states: guess, check and revise.

What if the child [or you] were given this problem:  3b = 7 +y  What would your balance look like when got it? Could someone else have ‘balanced’ theirs with a different arrangement?

How would your balance look if it solved this equation?  10 + x = 4 + y? Are there other arrangements? Why or why not?

The women in the church basement, sadly, never touched a balance with movable blue hangers. Had they, then ‘algebra’ would not have befuddled them so intensely as it did. Kindergarten ‘play’ could have helped them experience more success in their successive school days. Yet they, like me in the 50’s, never got the chance to touch and see the relationship of numbers as well as the concept of ‘equality.’ Oh, many of the left-brained students did, or the ones who were fortunate enough to have dedicated and clever math teachers. Yet so many are not clever and cannot understand why the students ‘don’t get’ their teaching.

For more examples of the use of the balance in kindergarten classes, watch the video below.

 

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7 thoughts on “Algebra for Kindergarten

  1. ||_(O)___\–+–/_||
    This is a rough drawing of the main bathroom in my former home in Old Orchard. The two lines at either end are the walls, the (0) is the toilet, the \–+–/ is the sink and the __ represents the floor. Like many houses built in the 50’s, there was a soffit overhead with a built-in fluorescent light.

    I wanted to update the look of the bathroom by removing the existing fluorescent light and installing recessed spotlights that would shine down over the toilet and sink. The was space enough for three separate spotlights. One light would be centered over the toilet, two lights centered over the sink, and all three lights would have an equal space between them.

    The carpenter didn’t have a clue. I remember kids saying “when will I ever use algebra again?” I used it that day.

    And the carpenter should have known how to use it (as much as he charged).

    1. remember kids saying “when will I ever use algebra again?” I used it that day.

      They didn’t know that they were using it because they never understood algebraic concepts in the first place. It was all rote, mechanical movements sans the intellect.

  2. “How would your balance look if it solved this equation? 10 + x = 4 + y? Are there other arrangements?”

    WTF, do I care, M_R? I had no use for it 50 years ago, nor do I think that I
    will have a use for it in the time we have left. All that crap in trig of sine,
    cosine, tangant is just that. Then, there was the good old slide rule, lolThen, came calculators and we were forbidden from using them, as it was a form of cheating, lol… I can support having a child learn basic mathematical concepts, but not all this algebra and trig crap. Maybe it is good for what our teachers called mental gymnastics!

  3. …not all this algebra and trig crap.

    Well, my luddite friend, the U.S. ranks 25 th out of 34 nations at a recent international mathematics scholarship event. That sucks! And we wonder why the U.S. is loosing its international edge?

    We hated math because we had terrible instructors who talked math rather than letting us explore math. What a waste of all of those miserable classroom hours!

  4. Yes, we did have poor math teachers. But, my friend, our scores were higher than most statistics today. Why? Could it be we were drilled on the fundamentals of math? Do you not remember the math game the nuns played with us, where the rows competed against each other to come up with the quiest correct answer, then that suddesful classmate gave up their seat and the next in line moved up and wchich row finished first got a treat or to go out first to the restroom or first in line to lucnch? Elementary and secondary education should not
    be preparing every single student for math and science higher education. To
    think that a college education is for every American is not accepting reality.

    As to being a luddite, how do you mean? Luddites were an English group who opposed the industrial revolution on the grounds that mechanization
    would cost them their jobs. I don’t have my head in the sand opposing
    progress. Maybe you wuld like to clarify what you meant?

    1. As to being a luddite, how do you mean?

      The term ‘luddite’ is now a METAPHOR for a person who resists change. You indicated that not all students ought to know x-amount of mathematics yet the jobs available for this math-deficient student are rendered the lowest rank of earning potential.

      You state, But, my friend, our scores were higher than most statistics today.

      No. What we ‘knew’ back in the mid 50’s can’t hold a candle to what kids in elementary school now know. We would flunk today’s proficiency tests required of students grades 3-12. We learned ARITHMETIC, not MATHEMATICS. We were equipped to become shopkeepers. We could never have become engineers with the shopkeepers arithmetic that we learned.

      All students can learn math if they are taught correctly using modern aids and with teachers who teach progressive lessons based on the most effective learning outcomes.

      That ‘game’ we played was I believe ‘baseball’ and all that it accomplished [mathematically] is that it proved who were good at mental math and who knew their arithmetic facts. You, as a severe left-brainer, found that exercise useful, but we right-brainers who are visual, not verbal, must reconstruct the voice message as a visual mental image before we can even begin to do the arithmetic.

      Children today whether right or left-brained are becoming primarily visual learners and therefore depend on visual cues for their learning. Babbling teachers who seldom use ‘the board’ [primitive] bore these kids to death. Believe me. I was there.

      1. “…must reconstruct the voice message as a visual mental image before we can even begin to do the arithmetic.”

        I have never been able to fully explain that to anyone. That’s how I do math. Straight A’s in high school math, an award from the State of Ohio for math, and I even scored a perfect on the college entrance math test. I can usually tell the right answer out of a group because it looks right to me or if the calculation is wrong because the answer doesn’t look right.

        Way back in kindergarten I remember when I learned numbers they all were distinct in their appearance. It’s almost as if they each had their own personality; actually they do. It’s always been a mystery to me why other people don’t see it that way.

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