Critical Thinking Skills
(or how Investigations fails to live up to its stated purpose)
I'm probably not qualified to write an article on critical thinking on a number of levels :) , but I'm going to just point out a couple of things that warrant discussion and see if it resonnates with anyone.
One of the stated purposes of Investigations Math is to raise critical thinking skills in children. It does this by teaching the "why" before the "how" when it comes to math problems. The belief is that if a person gains an appreciation for why math works, they'll be better able to do real problems when the time comes to actually put theory into practice.
There's no doubt that theory is completely integral to the performance of math skills. However, under the standard program of Investigations Math, it seems to delay the child from getting to the "how" stage for a really long time.
Now without getting religious, let me mention a religious talk given by an LDS leader that served as a member of the First Presidency (a counselor to the Prophet of the church). In 1938, J. Reuben Clark gave a talk entitled, "The Charted Course of the Church in Education." This landmark talk has been one of the guiding talks among LDS seminary and institute instructors for decades. In this talk, he emphatically outlines the desire of young people to be taught the gospel and not entertained. They want knowledge. They want instruction. I’d like to share a quote from this talk and then draw an analogy.
President Clark: “I wish to mention another thing that has happened in other lines, as a caution against the same thing happening in the Church educational system. On more than one occasion our Church members have gone to other places for special training in particular lines; they have had the training which was supposedly the last word, the most modern view, the new plus ultra of up-to-dateness; then they have brought it back and dosed it upon us without any thought as to whether we needed it or not. I refrain from mentioning well-known and, I believe, well-recognized instances of this sort of thing. I do not wish to wound any feelings.”
I suppose I am not as sensitive as President Clark in not wanting to offend. I wish to emphatically state that educators in Utah are fully asleep at the wheel in foisting these constructivist programs on our children. Who did the research before implementing these programs? Did we just blindly accept the sales job given to us to purchase and implement these programs?
Can you imagine having your local Bishop or Pastor say that all Sunday School classes for children will no longer teach moral absolutes, but the children will develop their own strategies for dealing with life's problems based on personal experiences? We'll just focus on the why and you figure out how to avoid problems. That same level of insanity is taking place in constructivist classrooms all over our country including Alpine School District. It is this level of “new plus ultra” thinking that is devastating our children who are eager and able to learn much more than is currently being given to them.
So what is critical thinking? To me, critical thinking is the ability to look at a complex situation and reduce it to it's simplest parts, and then be able to address each of those parts individually. It is taking a complex math problem and addressing the core aspects in a way that lets you reach the correct answer sought by the question.
The angle Investigations math takes is that critical thinking develops based on the students constructing their own theories about how math works. Children are forced to develop their way around math and then see if those theories are accurate. There are a few problems with this concept. First, there is precious little evidence that figuring out basic math algorithms actually produces critical thinking as opposed to basic thinking. Second, problems assigned from Investigations math don't reinforce the concept of critical thinking by giving the students problems that are so basic they don't require any multi-step vision of how to approach a problem.
(The following problems are pulled from an article by Ralph Raimi called "Why American Kids Aren't Learning Math")
For example, a sample math problem for Investigations Math suitable for 5th or 6th grade according to the Investigations Math book is:
Suppose you get 6 cents for each bottle you return for recycling.
You have collected 149 bottles. How much will you earn?
This is a single step problem easily identifiable as a multiplication problem. Multiply the numbers and you arrive at the answer. No critical thinking is needed to figure this out.
Opposite this is a 5th grade Singapore math problem which illustrates true critical thinking.
Adam bought 8 note pads at $1.45 each and 10 towels. He gave the cashier $100 and received $46 change. Find the cost of a towel.
In order to find the cost of the towel, the child has to do real critical thinking. The cost of a towel isn't given. This is a mini-puzzle. What is known is the quantity and price of another item and the cash and change exchanged with the cashier. The student has to calculate the total cost of the note pads, subtract the change from the amount given to the cashier to find how much was spent, and then subtract the cost of the note pads from the money spent, and then divide the remainder by the quantity of the towels to arrive at the cost of a towel. A FOUR step problem.
Now, which problem would you like your child developing their thinking skills with? Do you want them to struggle through 10 multiplication problems or do 3-4 of the more difficult problems that make them think about a variety of issues to arrive at the correct answer?
The Opposite's Fallacy
One of the biggest arguments you hear from people these days is that "that method is just rote memorization" or "we use an integrated method instead of fragmented teaching." These false arguments are damaging stereotypes of educational methods that so called "progressive" advocates use to denigrate traditional math.
The notion that Saxon or Singapore math just use rote memorization is completely false. True, they are fact and skill driven, but the problems given by Saxon or Singapore math are more comprehensive and the teaching methods combine all styles of teaching including use of manipulatives and discovery learning.
In an article called "Why Traditional Education Is More Progressive" by E.D. Hirsch, Dr. Hirsch states:
If parents were told straightforwardly that the so-called "untraditional" or "modern" mode of education now dominant in our schools has coincided with the decline of academic competencies among our students, they might be less enthusiastic about the experiment. When these dismal outcomes are pointed out, progressive educators usually reply that progressivism has never been tried "properly." (Oak note: see my page on the California failure to see this exact situation) That is false. It is merely the fail-safe defense that apologists use for all unsuccessful theories.
...In short, many progressive educational assertions that have attained the status of unquestioned fact by being repeated constantly are huge oversimplifications. They wither under close scrutiny. And they have done serious harm."
I'm not an expert on curriculum, nor have I reviewed many different math programs from different sources, but from what I have seen, I'd choose Saxon or Singapore math any day of the week, month, or year over Investigation's watered down problems (and Connected and Interactive Math). There's nothing to challenge kids in that curricula and it's a real shame that the Alpine school board is condemning 52,000 children to sub-standard math skills for the rest of their lives. The only thing that can save these children is homeschooling and tutoring in conjunction with the school programs and then the school district will take the credit for what the parents are doing to save their child's math education.
Our children want knowledge and they are ready and able to be taught. Critical thinking is an acquired skill that comes by analysis as you get older. I believe it is inappropriate to attempt to teach critical thinking to young children in the manner constructivist programs advocate. Teach children their facts and as they get older give them harder problems to solve and they will develop all the skills they need. Incorporate it into the curriculum so the students practice it regularly. It has to be part of the training they get and the homework they do.
For further enlightenment about this topic, read what parents are saying on these pages:
Investigations Math poll comments
Community Comments after the poll emailed to me
Thomas Sowell also wrote an excellent article on not holding back bright students. Here's a link and clip from the article if you want to check it out:
Bright Students Deserve More Than Busy Work by Thomas Sowell
" High potential will remain only potential unless it is developed. But the very thought that high potential should be developed more fully never seems to occur to many of our educators — and some are absolutely hostile to the idea.
It violates their notions of equality or "social justice," and it threatens the "self-esteem" of other students. As a result, too often a student with the potential to become a future scientist, inventor or a discoverer of a cure for cancer will instead have his time tied up doing busy work for the teacher.
Even so-called "gifted and talented" programs often turn out to be simply a bigger load of the same level of work that other students are doing — keeping the brighter students busy in a separate room.
Investigations Math Menu
** Most important pages to read (all have value but if you will only read
a few pages make it these)
* Very important