COMING SOON "Ask The Expert" live event w/ the CC Dean, Sally Rubenstone, on Feb. 22 at 12:00 pm ET. This event is exclusively for registered members. CREATE YOUR CC ACCOUNT NOW to receive event updates!

# Math Placement Test Without a Calculator?

This discussion has been closed.

## Replies to: Math Placement Test Without a Calculator?

Yes it is, as it should be.

Calculators can be very useful in many situations and I by no means would suggest banning them completely from the classroom, but if one can't perform basic maths without a calculator then yes a remedial maths course seems only appropriate.

http://en.wikipedia.org/wiki/Newton%27s_method#Square_root_of_a_number

The Secant Method (I think that I can imagine how that works)

Lin's method

Graeffe's method

Bernoulli's method

Laguerre's method

Muller's method

There are references to four additional books for further methods. There are also some methods described in the exercises. Most of these methods are generally aimed at solving polynomials, not finding square roots.

There is one notable approach with an iteration formula that converges cubically but the arithmetic is more complicated than Newton's method.

I think that Newton's method is best for doing hand square roots. It's easy to remember, converges quickly and doesn't entail complicated arithmetic.

Consider Javascript which has to handle numbers with arbitrary bases. So it has to handle hex numbers where digits go from 0-9 and A-F and either switch back and forth between integers or floating point numbers or just manage the math in the human representation. It's more coding work but I wouldn't call it difficult.

Calculate square root without a calculator

I know in my BC Calc class we've only has 1-2 exams where we could use calculators, and for one of them it was only part of the exam.

Calcs are great for chem... I try and avoid them for math. I've been really lucky in having great teachers who test on theory and not number crunching, although pre-highschool was terrible. Middle school math teachers are the worst tbh...

Here's a question that used to be on our standardized test but was "released" and is able to be used for examples.

"Mrs. Smith put her students into groups. One sixth of the students were in each group. How many groups were there?"

What grade do you think I teach? (okay I'll just say it) I teach second graders, 7 year olds. This is a very simple question if the students understand the concept of fractions. If not, there will be problem.

When my kids try to cut corners and not learn the process because the smaller number is easy to do by counting up or something instead of working the process on paper, I show them a much larger problem and dare them to try it their way. Once they understand the numbers and how the process works they can do anything. They love harder and harder problems!

Here's the thing, though. Assuming that the 22 on the ACT (roughly comparable to a 520 on the Math SAT) is a correct assessment of your daughter's math ability at this time, she's not yet ready to take calculus. She needs the remedial class. People with 22 ACTs don't know enough algebra to be able to do calculus. This has nothing to do with calculators. If she took the calculus class right now, she probably wouldn't pass it.

Discrete Probability would be a challenge too, I imagine. Those probability and counting problems require some mathematical imagination.

And if she can't come up with a pretty good estimate of the square root of 95 without a calculator in her hands, that's good evidence that the placement test was perfectly correct.

I recall my sophomore year in college, when I was a teaching assistant in sociology. I was very concerned that many of the short answers for class assignments were very poorly written (hard to even understand what they students were trying to convey) and shyly suggested to some of the students that they consider taking English courses. A few of the students were quite offended and proudly said that their English teachers considered them great writers (made me shudder).

I also remember a college statistics course for non-science majors I took where some people asked if we could form a study group and I could lead it. Neither of the other students knew the relationship between a fraction and a decimal. By the end of the term, they both had a good understanding of statistics, acquired SOME number sense and all of us got As in the course.

> is easy to do by counting up or something instead of working the process on paper, I

> show them a much larger problem and dare them to try it their way. Once they

> understand the numbers and how the process works they can do anything. They love

> harder and harder problems!

Fractions are a big problem area in elementary-level arithmetic. I have seen students that

have trouble with problems involving fractions because their calculators don't natively

represent them in any form other than as decimals.

Fractions are quite complicated as presented. Adults usually don't see it that way as they

are familiar with the implicit framework around fractional operations.

- We assume the decimal numbering system. I think that most would have difficulty doing fractional operations in base 16 or base 11. Most would probably convert to base 10, do the arithmetic and then convert back to the original base instead of working natively in the other base.

- We assume a certain amount of the rules of number theory. When we see 15/40, we mentally simplify because we know that there is a common factor to the numerator and denominator.

- Many people, children and adults, have trouble adding fractions with dissimilar denominators. The algebra is fairly simple for those that remember it but sometimes you don't want to work with large numbers (the product of denominators) so you try some factorizations. There are processes, procedures and algorithms that adults take for granted that kids don't know.

In elementary school, we teach kids facts and procedures and sometimes we toss in properties. In general, I don't believe that the terms associative, commutative, distributive, existence, identity and inverse are used but the ideas are. They are presented as laws or facts implicitly in the process of learning to do operations. Most adults do operations knowing these things implicitly. Many are aware of them as they are covered in middle-school and high-school but they are not covered in a formal way. The first chapter of Spivak's Calculus does a pretty good job at introducing the student to a more formal understanding of arithmetic.

It isn't surprising that a lot of students get confused in fractions as they don't see the whole picture and framework. They can certainly learn fractions well enough so that they become proficient in operations but I sometimes wonder if the process would be better with exposing young children to some of the formal stuff.

So true. At my institution, a student wouldn't be considered calc-ready after the remedial series. She'd be ready for stat, discrete math, math for liberal arts (and before you pooh-pooh it, let me tell you it's a tough course), but would still have another prerequisite before calc.

And himom, yeah, remedial English really isn't much different than math. Students are insulted when they get placed because their honors or AP English teacher was really good (we don't give comp credit for AP) Yet, the need is very great. I know some hs English teachers, and have no doubt they are very good, but they're under a lot of pressure to give high grades and give students opportunities to improve their grades. As in math, students come in thinking they're much better than they are. OD2's lowest grade this semester was in English. I'm not saying a word, no meeting with the teacher, nothing. English isn't her thing (she's a math kid) and she 's not as good at it as some of her peers.