Posted on 08/10/2010 10:13:25 AM PDT by decimon
COLLEGE STATION, Aug. 10, 2010 — Taken very literally, not all students are created equal—especially in their math learning skills, say Texas A&M University researchers who have found that not fully understanding the “equal sign” in a math problem could be a key to why U.S. students underperform their peers from other countries in math.
“About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students,” note Robert M. Capraro and Mary Capraro of the Department of Teaching, Learning, and Culture at Texas A&M.
They have been trying to evaluate the success of math education through students’ interpretation of the equal sign. They have published several articles on this topic, with the most recent one published in the February 2010 issue of the journal Psychological Reports.
Students who exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering, according to their research.
“The equal sign is pervasive and fundamentally linked to mathematics from kindergarten through upper-level calculus,” Robert M. Capraro says. “The idea of symbols that convey relative meaning, such as the equal sign and “less than” and “greater than” signs, is complex and they serve as a precursor to ideas of variables, which also require the same level of abstract thinking.”
The problem is students memorize procedures without fully understanding the mathematics, he notes.
“Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer,” he explains. “So the work would look like 4+3+2=(9)+2=11.
“This response has been called a running equal sign—similar to how a calculator might work when the numbers and equal sign are entered as they appear in the sentence,” he explains. “However, this understanding is incorrect. The correct solution makes both sides equal. So the understanding should be 4+3+2=(7)+2. Now both sides of the equal sign equal 9.”
One cause of the problem might be the textbooks, the research shows.
The Texas A&M researchers examined textbooks in China and the United States and found “Chinese textbooks provided the best examples for students and that even the best U.S. textbooks, those sponsored by the National Science Foundation, were lacking relational examples about the equal sign.”
Parents and teachers can help the students. The two researchers suggest using mathematics manipulatives and encourage teachers “to read professional journals, become informed about the problem and modify their instruction.”
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About research at Texas A&M University: As one of the world’s leading research institutions, Texas A&M is in the vanguard in making significant contributions to the storehouse of knowledge, including that of science and technology. Research conducted at Texas A&M represents an annual investment of more than $582 million, which ranks third nationally for universities without a medical school, and underwrites approximately 3,500 sponsored projects. That research creates new knowledge that provides basic, fundamental and applied contributions resulting in many cases in economic benefits to the state, nation and world.
Contact: Keith Randall, News & Information Services, at (979) 845-4644; or Robert M. Capraro, Department of Teaching, Learning, and Culture, at (979) 845-8007; or Miao Jingang, News & Information Services.
For the dumbed down Everyday Math, the REQUIRE calculators in kinderarten! No kidding. It’s another way to reach an indiidual “learning style”, so they say. THEN they started to realize that on the NJASK test, their state test, that MAYBE, just MAYBE the kids really don’t know their mulitiplication facts. Mine aren’t in a public school because of this craay crap. We sacrfice to make sure they get an EDUCATION and KNOW something of value. So NEVER, EVER believe New Jersey PUBLIC schools are wonderful - they are not!
My experience is that about 1 in 30 students will pick up programming easy peasy, while the rest will never get it.
“I believe they are purposely CONFUSING students so they don’t KNOW anything.”
My kids were being taught some goofy math. My wife went in and started just doing math memorization facts with the entire class because it wasn’t covered in the curriculum! The teachers were NOT supposed to teach it! But, they did let my wife teach it.
The curriculum called for math like this (I kid you not, and I had a real hard time with it!!)
36 + 12 = ?
Well 36 is about 40, and 12 is about 10, so:
40 + 10 = 50.
But, 40-36 = 4, so take away 4 from 50:
50-4=46.
But 12, is 2 more than 10, so you have to add that back in:
46+2 = 48. ANSWER!
They even made you show the work. My one daughter could do it the goofy way, my other couldn’t (but could do it the “regular” way). She would get marked down doing it the regular way. We went in and told the teacher at the time that if she got the correct answer it was correct. And we didn’t care how the teacher marked it.
They (teachers included) are trying to get the curriculum changed, but it will still be a few years.
In kindergarten, they start them on calculators. No kidding. Between that and the collaborative learning method which is closely related to the cooperative learning method that failed miserably. It is used in nearly ALL subjects. It is GROUP THINK and a GROUP grade. Imagine how much EASIER that is for a “teacher”. They don't have to “teach” because kids teach each other and less grading to do when kids do NOT grade their GROUP work.
“Collaborative learning is a situation in which two or more people learn or attempt to learn something together.[1] More specifically, collaborative learning is based on the model that knowledge can be created within a population where members actively interact by sharing experiences and take on asymmetry roles.[2] Put differently, collaborative learning refers to methodologies and environments in which learners engage in a common task where each individual depends on and is accountable to each other. Collaborative learning is heavily rooted in Vygotsky’s views that there exists an inherent social nature of learning which is shown through his theory of zone of proximal development.[3] Often, collaborative learning is used as an umbrella term for a variety of approaches in education that involve joint intellectual effort by students or students and teachers.[4] Thus, collaborative learning is commonly illustrated when groups of students work together to search for understanding, meaning, or solutions or to create an artifact or product of their learning. Further, collaborative learning redefines traditional student-teacher relationship in the classroom which results in controversy over whether this paradigm is more beneficial than harmful.[5] Collaborative learning activities can include collaborative writing, group projects, joint problem solving, debates, study teams,and other activities. The approach is closely related to cooperative learning.”
http://en.wikipedia.org/wiki/Collaborative_learning
It destroys the INDIVIDUAL, erases their self confidence and kids that are bright have to TEACH other kids or else. Part of the grade also includes a SOCIAL component. If a kids doesn't want to be stuck with a lazy kid or a stupid kid and it shows, the bright kid gets a reduced grade! Isn't that nifty?
Here's video on what the result of this is:
http://www.youtube.com/watch?v=Tr1qee-bTZI
NOTICE the curriculum's she does NOT RECOMMEND.
Yes, kids are supposed to DISCOVER it.
Teachers are NOT supposed to TEACH it.
What they do is get into their GROUPS and teach each other math. If a kid has a question and musters up the courage to ASK the TEACHER - the TEACHER will simply ask them another QUESTION. The TEACHER is NOT supposed to TEACH or ANSWER QUESTIONS. The kids must reinvent math and figure it out as a GROUP.
This is just so stupid. The concept of equals if ridiculously simple. The only reasons a kid should not know it is because NOBODY ever explained it to him. That includes teachers and parents.
I can explain it to a 6 year old in two minutes.
Division is even more fun!
It's totally convoluted and not explained well. At best it should be a pop corn box on a Math page. When properly explained it does show the relationships in math but it is not explained properly. Traditional math must be what they get back to.
We pay through the nose to avoid this crap. We stay with traditional math and they're in the Johns Hopkins program which has some of it but is more tradition math based. What we like about CTY math programs is it is geared to the individual - no group work and prgress is charted by category within the subject.
Look into it:
http://cty.jhu.edu/ts/tests.html
It's an international program and the url above shows how to qualify for it and then test into their program.
Hah! No surprise to you I’m sure that I am in Washington State!
What is really sad is that MOST parents don’t get involved in their kid’s education and just let the schools do it. Math is a huge one in our family where we need to help the kids. Social studies is another when it comes to some of the issues. (My one daughter did a poster board for the 5th grade science fair showing how the manmade global warming stuff was wrong!)
As for myself and our daughter we have her learning traditional math and expose her to the “new” math. When she has the traditional math under her belt, then she can understand what they are trying to do with the “new” math. They are not teaching the “new” math properly.
The "new" math is okay but we don't spend much time with it. It's confusing to kids without traditional math as a foundation and not really useful.
We also parallel traditional math with Singapore Math. Between the two we are satisfied. may California school use Singapore Math as their Math curriculum.
Here's the legitimate Singapore Math site:
http://www.singaporemath.com/Default.asp?Redirected=Y
We're in over taxed and undereducated New Jersey. The education here is a MESS. If anyone can afford it, they keep their kids OUT of the New Jersey PUBLIC SCHOOLS. They ALL stink.
“What is really sad is that MOST parents don’t get involved in their kid’s education and just let the schools do it.”
That is a SAD FACT. I don't understand it.
“Math is a huge one in our family where we need to help the kids. Social studies is another when it comes to some of the issues. (My one daughter did a poster board for the 5th grade science fair showing how the manmade global warming stuff was wrong!)”
Tell your kids they have OUTSTANDING PARENTS! you truly are. Most parents have no clue on what is going on.
I LOVE your daughter already!!!!! Please give her my highest compleiments. We need MORE LIKE HER!!!!!! She is a treasure.
BTW, I came across something else you might find useful. I will use this to compliment social studies that used to be called history ... .
America's Heritage: An Adventure in Liberty
K-12 Teacher Lesson Plan Resource
$150.00 value!
Order Lesson Plan CD (free!) or printed binders
America's Heritage: An Adventure in Liberty is a tested lesson plan resource and supplement for Kindergarten-12th grade teachers of social studies, U. S. history, U. S. government, political science, economics, geography, speech, and/or related subjects. Written by fellow teachers, the resource consists of age-appropriate and modifiable lesson plans grouped into three separate books according to level: elementary, middle, and high school. Each elementary school lesson plan correlates practically with the nationally applicable Core Knowledge Skills (grades K-6) (national edition). Each middle and high school lesson plan correlates with the National Council for the Social Studies (NCSS) standards (national edition). All lessons emphasize one or more themes of freedom, unity, progress, and responsibility. The resource aims not simply to present historical facts but to provide opportunities for students to explore and understand the factual and philosophical significance and meaning behind events, causes, and effects—the whys—relating to and influencing the early history of the United States.
Each resource book includes an introductory essay regarding the curriculum rationale, lesson plans to specifically consider the American heritage themes, and activities in which students assess and analyze their own identities as Americans. The elementary school lesson plans include lessons about the colonists’ experience under monarchy; the context for the writing of the Declaration of Independence; the creation of important American symbols, songs, and holidays; and the character traits modeled by great national leaders and presidents. The middle school lesson plans include lessons focusing on concepts within the Declaration of Independence, the Gettysburg Address, and other important texts and American symbols as well as the ideals for which many fought and sacrificed their lives. The high school lesson plans include lessons for in-depth analysis and understanding of the ideas, intentions, arguments, rights, and meanings addressed in significant texts from the Mayflower Compact and the Declaration of Independence to Federalist 47, the First Amendment, and a government letter on religious expression in public schools. A brief summary of each lesson plan can be found at the appropriate grade-level links.
America's Heritage has been evaluated in a study for performance results of students of eighth-grade social studies as indicated by the Texas Assessment of Academic Skills (TAAS), a test measuring American history objectives taught by schools around the nation. Consistent with the goals of AHEF, the study showed a positive learning difference based on TAAS results with regard to historical concepts and information in students whose teachers used America's Heritage. These findings demonstrate the value for teachers in using the resource to increase student performance as measured on the TAAS.
2nd Assessment (2003)
Student Performance Results of Teachers Trained In and Using
America's Heritage: An Adventure in Liberty
An evaluation of student performance was made with data from the Spring 2003 administration of the Texas Assessment of Academic Skills (TAAS) comparing performance of students of teachers trained in and using America's Heritage with students of teachers who have not had training in or used this resource. There was a statistically significant difference for the experimental subgroup of Hispanics on the objective Economic and Social Influences in U. S. History on the Texas Assessment of Academic Skills (TAAS). The study indicates that Hispanic students whose teachers were trained in and used the resource increased in performance in the objective Economic and Social Influences in U. S. History on the Texas Assessment of Academic Skills (TAAS). This finding is important for schools and teachers seeking to reduce the achievement gap between Hispanics and other ethnic groups, with Hispanics being the fastest growing sub-population in the United States.
See 2nd Resource Evaluation Study.
1st Assessment (2002)
Student Performance Results of Teachers Using
America's Heritage: An Adventure in Liberty
America's Heritage was evaluated for 2002 performance results of students of 8th-grade social studies as indicated by the Texas Assessment of Academic Skills (TAAS), a test measuring American history objectives taught by schools around the nation. Consistent with the goals of AHEF, the study shows that students whose teachers use America's Heritage increase in performance in social studies historical concepts and information as measured on the TAAS. These findings demonstrate the value for teachers in using the resource to increase student performance.
See 1st Resource Evaluation Study .
http://www.americanheritage.org/k-12_lessons.html
Scroll down on the same url and choose what interests you:
Elementary School Lesson Plans
Middle School Lesson Plans
High School Lesson Plans I will be using this as supplementary material. Pass it along if you know of others that might be interested.
Worse still, in various programing languages, when a=4 and b=3, then a+=b is 7.
ping
Heh. Along with math facts, schools should teach the use of the dictionary.
Those “ob-” words say so much! Everyone should have an unabridged dictionary, just to pass the time. Flummox your neighbors *and* get a great SAT score!
Fundamental failure of first 3 years of schooling.
Using Mathematica or similar to graph functions is trivial.
Learning to find the zero crossings, find the inflection points, and sketch in the function’s curve yourself leads to improved mastery.
I still remember being taught “estimating” way back whenever it was. Even then it was apparent that the issue was grossly misplaced, and whoever wrote the text was unclear on how to get the point across (but had to write _something_).
Long after, I understood that estimation is a technique which can ONLY be done when you know the subject so well you have the innate feel of how you can kick things around to get a good-enough result.
Teaching estimation by rigor is incompetence manifest.
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