Warren Wolff • In the CA high schools where I taught, students did not escape my classes without some decent math skills which included thought processes. Sadly, the attitude of most administrators was that you were a baaaad teacher if you failed students. I know of one administrator who would not keep you on staff unless half of your students had a C or above - - regardless of student performance. When students arrived in my freshman algebra class, I had a little "entrance exam". I found that only one our of three knew what 8 x 7 = - - - - AND thought 1/3 + 1/3 = 2/6 [some reducing this to 1/3] ! ! ! ! I was reasonable successful in correcting these deficiencies. In my classes , we did discuss asset allocation, checking, inflation, et al. Hopefully they are a better lot today. Many of my ex- students have "found me" - - even the "F" students who have apologized and proudly presented themselves as far better off today, partly do to my "pushy attitude" in the classroom.
Robin Yang • Warren, I applaud your effort of teaching kids financial literacy and math at the same time. It is sad that teachers at lower grades are forced to pass students who shouldn't have passed, thus causing students poorly prepared for higher grades, colleges, or career. Another problem is that teachers are not allowed to assign homework during long summer vacations. So students forget what they've learned after three months of no school and no homework. That's why I think one solution to remediate the current problems is to inspire students to practice math on their own in their spare time. Check out this article for more details. http://enchantedcollar.com/math-homework/
I teach a so called college algebra class in a community college. Like you, I often start with a simple question, just to give them a feeling of confidence. So the first question asked the student to divide 36 by 17 and give me an eight place answer.
The student writes down: 2.29411765 Clearly the wrong answer. To check the answer, I enter the digits into my calculator, multiply by 17 (like I tell them they should be doing) and I get 39.00000005 Instead of dividing 36 they divided 39.
So what can I do that will encourage them to be more careful in the future? Do I (a) tell them that was a stupid mistake (b) give them partial credit for entering 5 of the six key strokes correctly? (c) make some sarcastic comment about maybe holding the calculator upside down and the nine looked like a six (d) talk about "fat fingering" the calculator since the 9 is so close to the six. (e) discuss whether 0.7647 was within the margin of error for this operation (f) repeat my admonitions about checking their answers (g) encourage them (again) to review what they entered into the calculator
Our district has adopted Key Performance Indicators emphasizing completion rates and our new contract has incentives based on student success. Maybe I should just give them all an "A" to make sure I qualify for the bonus?
Robin Yang • Julius, thank you for your interesting comment! I will be interested to learn what you ended up doing in the situation you described. I have found that American students are dependent on calculators from elementary school onward and thus never bothered to master the basic math concepts. They've never learned simple techniques of guestimating because they never bothered to calculate numbers in their heads. Do you think allowing students to use calculators in elementary math classes partially contributed to students' poor performance in higher grades?
Janice Hodgson • I agree that the use of calculators in the younger grades will contribute to poor performance in the higher grades if they are being used for more than just a tool for checking their work. Unfortunately, too many are using calculators to expedite the completion of problems. The push for critical thinking at all levels has forced some teachers to sacrafice the arithmetic for the problem-solving process. For example, I have had classes of students who have never learned long-division. Many students that I have had over the years [particularly the last 15 years] do not know their multiplication tables. The trend to abandon rote memory as a tool to learning basic Math skills is frightening. To answer the original question..."Can children learn fiscal responsibility without Math proficiency?"...I think they can...at a certain level. I currently teach a Personal Financial Math class to juniors and seniors in my high school. Many of these students take this class because they have had difficulty in Math in the past and feel they cannot take Pre-calculus, or IB Math, or AP Statistics. In some cases, they don't even take Algebra II with Trigonometry. Many of these students are what some may call "Math-phobic". With all that said, these students emerge from this full year course with a very good grasp on fiscal resonsibility through instruction on Budgeting; Banking [including balancing a checkbook and managing different types of savings accounts]; Credit and Debit cards; Credit Score and Credit reports; Income taxes; Payroll taxes; Purchasing a home vs. Renting; Buying a car vs. Leasing; Student Loans; Bankrutcy; Investments and Retirement. In this course, they learn how to navigate the internet to research some of these topics and they learn how to properly use a calculator when needed for certain units. Obviously, these students need to know when to add, subtract, multiply, divide, change a percent to a decimal, and other basic arithmetic skills. These are things that can be reviewed as the unit is being taught. Do they need basic math skills? Yes, absolutely! "Math Proficiency"? I don't think so. [Sorry for the lengthy response.]
David Ball • Understanding trumps routine. A good lesson doesn't have to be numerical. When it comes to memory and performance, the tried and known will still fail the same way. While the experimental has new ways to succeed and fail. A bad lesson is primarily drill for no purpose. When I work with junior high school kids school years 7-9, as a Maths teacher, my focus is on the concepts, not the numbers. Tom Lehrer once joked 'it was more important to know what your are doing rather than to get the right answers'. People provide one off examples of failure. In fact unless the focus is solely on the teacher, which is eschewed in modern pedagogy, many mistakes are always quickly made. Those who remember are the successes. Those who remember the techniques without the way of achieving it .. blessed.
decent math skills which included thought processes. Sadly, the attitude of most administrators was that you were a baaaad teacher if you failed students. I know of one administrator who would not keep you on staff unless half of your students had a C or above - - regardless of student performance. When students arrived in my freshman algebra class, I had a little "entrance exam". I found that only one our of three knew what 8 x 7 = - - - - AND thought 1/3 + 1/3 = 2/6 [some reducing this to 1/3] ! ! ! ! I was reasonable successful in correcting these deficiencies. In my classes , we did discuss asset allocation, checking, inflation, et al. Hopefully they are a better lot today. Many of my ex- students have "found me" - - even the "F" students who have apologized and proudly presented themselves as far better off today, partly do to my "pushy attitude" in the classroom.
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1I teach a so called college algebra class in a community college. Like you, I often start with a simple question, just to give them a feeling of confidence. So the first question asked the student to divide 36 by 17 and give me an eight place answer.
The student writes down: 2.29411765
Clearly the wrong answer.
To check the answer, I enter the digits into my calculator, multiply
by 17 (like I tell them they should be doing) and I get 39.00000005
Instead of dividing 36 they divided 39.
So what can I do that will encourage them to be more careful in the future?
Do I
(a) tell them that was a stupid mistake
(b) give them partial credit for entering 5 of the six key strokes correctly?
(c) make some sarcastic comment about maybe holding the calculator upside down and the nine looked like a six
(d) talk about "fat fingering" the calculator since the 9 is so close to the six.
(e) discuss whether 0.7647 was within the margin of error for this operation
(f) repeat my admonitions about checking their answers
(g) encourage them (again) to review what they entered into the calculator
Our district has adopted Key Performance Indicators emphasizing completion rates and our new contract has incentives based on student success. Maybe I should just give them all an "A" to make sure I qualify for the bonus?
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