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If you think that 3 x 4 = 12, you might want to think again. With the new Common Core Curriculum Math, 3 x 4 can = 11 or 7 or 235, as long as your child can “show the work to defend their answer.”
But, of course, this is so necessary in today’s dystopian world. You see, if 3 x 4 = 12, that is truth. And to acknowledge objective truth in this relativistic world in which we live is so very dangerous. Because if there is truth, then that opens the incredibly dangerous thought that there just might be Truth. And, of course, Christians know that Truth is not a word. Truth is a Person. Truth is our Lord and Savior Jesus Christ. And, certainly, we can’t have any young, impressionable young mind encountering Him in their educational pursuits.
I cannot help but be reminded of Shakespeare’s Macbeth (“Fair is foul and foul is fair”) or George Orwell’s 1984 (“2 + 2 = 5″). Oh, but don’t worry. With the Common Core curriculum, the only form of Shakespeare your kids will be reading will be “annotated excerpts” and “condensed versions”. You see, as we work our way (more quickly every day now) towards Bill and Melinda Gates’ idyllic “iPads for every child” and “textbook-free schools,” all in the name of “technological advancement,” it becomes ever so easy to manipulate words, data and, thus, ultimately, truth. Step by step, words and data are manipulated, revised, edited and deleted until, one day, we wake up and our kids are being fed an education based on “truths” like 3 x 4 = 11.
Oh wait, that day is here.
12 thoughts on “The Death of Truth in Catholic Schools?”
Sure 3×4=11, in base eleven. And that is Truth. If a second- or third-grade pupil of mine can show me that he understands the concept of number bases and the use of base eleven was his intention (rather than a blunder) then he’s a very remarkable child and much closer to the whole of mathematical truth than his classmates.
P.S. My first exposure to alternative number bases was in a Catholic parochial school.
How many defending the Common Core Curriculum would consent to a procedure by a surgeon trained similarly?
P.S. Doc, stumbled across some of your writing this a.m. nice work.
I’m a veteran of the math wars in the ‘00s.
Yes, it’s possible K-8 math curriculums selected for the
Common Core will be better than the constructivist mathematics programs like
Investigations, Everyday Math, and Trailblazers.
But there is a very long history. You can start at Mathematically Incorrect,
the granddaddy site; you can google constructivism. A lot of parents spent a lot of time
detailing what is wrong with constructivism, and how it falls short of its
stated goals, and posting their work online as they fought to keep these
curriculums out of public schools.
However, just for the sake of discussion of this recent
video, let me suggest a few problems with 3×4=11.
1.
Young teachers are hapless victims of
ideologically motivated older teachers and education professors who are
promoting a world view. Young teachers
don’t know any better than to repeat the best practices catechesis they
received in school and at professional development.
2.
Young teachers do not realize, nor do young
parents, that one teacher in a classroom of thirty children will not have the
time to thoughtfully and constructively correct each child’s persuasive
argument that 3×4=11. They will merely
give credit. A point. A smiley face. There is no time for a teacher to teach each
child how to write out an argument.
3.
Telling young teachers to give points for a
persuasive argument results in every child getting a point for any written
explanation, good or bad or indifferent.
Which has the effect of teaching children to value persuasion, measured
by the number of words, rather than to seek truth. Trust me.
I helped teachers grade these very problems. Close is always good enough to get points, if
the child appears sincere.
4.
On the other hand, asking children to seek the
right answer, in this case the number 12, teaches children that an objective
truth exists outside of them, outside of their teacher, outside of their parents. We reason, and we think truth can be known
through reason. In short, arithmetic is
the child’s first real apprehension of an objective truth that is not relative
to socially constructed relationships.
My dad may be bigger than me, but 3×4=12 for him, too.
5.
The worldview of many older teachers and
education professors is that there is no objective truth, and mathematics is
just one of many socially constructed relationships that allocate power. They value persuasion over the reason, and
they want to teach their little troops the same. There is nothing kind or considerate about
treating children this way.
Nice post, but consider:
Re: 1–“Young teachers are hapless victims of ideologically motivated older teachers and education professors who are promoting a world view.”
This is too general, as it seems to imply teaching would be static: weren’t those older teacher once young? How did THEY get from hapless to ideologically motivated?
Re: 2–I agree, but if one method is pedagogically sounder than the other but requires smaller class sizes, why not spend the ducats to get it right?
Re: 3 & 4–
Teaching Johnny and Sarah why 3X4=12:
Take a group of 3: {@,@,@}
Now repeat it 4 times: {@,@,@} {@,@,@} {@,@,@} {@,@,@}
Now count the ‘@’s: See Johnny you left out an ‘@’, and Sarah you have one too many.
Why not simply recalibrate the measuring stick for the diagnostic? Johnny and Sarah get 7 of 10 for reasoning, those who reason correctly instead of 10 of 10. Not that hard.
Re: 5–I went through those culture wars but academics is no longer stuck there. There are some holdouts, but it is generally acknowledged that there are truths that cross all or most cultural lines, and even lines of species (google ‘pigeons counting’).
Finally, I think your post confuses constructivism or intuitionism with methods like the one I’ve listed above. Constructivism is a new program viewed with an interested skepticism by most logicians and mathematicians, at least in my experience. I know, from first hand experience, that many abuse the concepts of these projects to uphold their own views. But this is not new, Renaissance thinkers did the same with Pythagoras. It proved wrong then and it will prove wrong now, but not for the reasons I see listed here.
The method I used above, BTW, antedates constructivism or intuitionism—I find it dates back at least to Descartes but wouldn’t be surprised if it was used by a Greek thinker.
My hope for this post is that people pause to think about what is going on here. There is a lot at stake, but creating straw man arguments or dragging red herrings up does not help us get to the truth of the matter.
I have first-person experience with several young teachers, and I choose the word “hapless” carefully. Some teachers tried gamely to defend the programs in order to advance their careers; some kept their heads down. That is all.
We do not have the money to assign one Socrates to each child. That is what homeschooling is for.
There is no time in the school day to lovingly assign points as you suggest.
My post does not confuse constructivism with anything else. I went to the original sources. I’ve read my Constance Kamii.
No straw men. No red herrings.
I kept my post short. I’ll keep this reply short.
But multiplication is not a “process”. Certainly some examples showing that multiplication is repeated addition is fine, and a child who can express that is fine, but I think that too much emphasis on the “process” of basic math concepts just impedes the flow of thought in dealing with math. 3 x 4 = 12. How do I know that? Because I know how to multiply and I have bothered to learn the multiplication tables. Next question.
I actually do agree with you that an emphasis on process is not necessarily a good thing, although in the math curriculum we have used (Math U See, which is a top rated program) there is quite a bit of “teaching back” that goes on at the younger grades.
But the point is this: this is 43 seconds out of a presentation that we 1) don’t know how long it really was or 2) exactly what they had been speaking about before they got into this particular example. What was the broader context? Coming up with universal standards for education is an idea worth exploring, but I have grave doubts as to this attempt at implementation. There is the whole “Federal government take over of education,” angle, the “standardized testing” angle, “data mining,” etc. We need good solid arguments to defeat Common Core. Perhaps this is an effective sound bite–it is certainly making its way around the web. But what if I am a policy maker, and I see the entire presentation, and it is something other than just this 43 seconds-and a lot of it good stuff. If someone came to me and said “Hey, look, under Common Core, our kids are going to learn 3×4=11 is okay.” Well, that person doesn’t sound like they done their homework.
“they’ve done their homework.”
Perhaps that is so in the cases of pairs of small multiplicands the products of which one has committed to memory. For pairs of large numbers, I strongly disagree.
By the way, in my grandparents’ day students were expected to memorize multiplication tables through 16×16. Standards were relaxed when I was a grade schooler, I was expected to commit to memory only the table through 12×12. My younger cousins encountered further dumbing-down, they were only expected to memorize the table up to 10×10. By the 1990s I encountered schools using textbooks that merely introduced pupils to the multiplication table and required memorization of little more of the table than up to 5×5.
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The cited video is 43 seconds out of a much longer presentation; there just isn’t much context here. How old are the children in question? Are they gifted and talented, dyslexic or other LD? Developmentally Disabled in some fashion? As a homeschooler, I’ve used a program which, as part of the program, has the students explain back how to do the problems, orally, with the blocks or other manipulatives, etc. It has happened to me, and I am sure to others, where a young child might very well come up with a wrong answer (3X4=11), but the picture he drew or the blocks he put together, his answer is very clearly 3×4=12 and he misspoke or miscopied or something. The presenter very clearly stated erroneous answers are to be corrected, and they “want the students to compute correctly.” She does go on to say “we’re more focused on the how and the why,” but without a broader context, It is difficult for me to consign “Common Core” math to the dust bin (at least based on these 43 seconds.)
Common Core is problematic, but I am not sure this particular video snippet is a good way to attack it. As Catholics, I think we are all very used to, and a little tired of “Bible Christians” pulling this verse or that verse out of the Bible, taking it out of context and using it to attack our faith (“How can you corrupt Catholics call a priest “Father” when Jesus said “Call no man ‘father’.?!)
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