Students have used paper and pencil for years. Undoubtedly,we all used paper and pencil in all of our studies in all subjects and particularly in our practice in mathematics, both in the elemental and advanced branches. Now we are told that paper and pencil are no longer necessary in our traditional classrooms. Yet, they are used in 'new math' classroom for all sorts of "discovery activities" and used freely. Very freely.

Below are examples of such "paper and pencil" activities, taken from Passport to Mathematics, Book 1, by McDougal Littell, 1999 Ed.

From Lesson 1:

MATH JOURNAL

Have students use a separate notebook or a binder for their math journal writing for the school year.

Have students describe the reasoning they used at each step in the Lesson Investigation.

At each step of the Lesson?

I really want to go now to Lesson 2.

ECONOMICS In Exercises 1-3, use the information in the newspaper article at the right. The article is comparing the costs of buying various items in three towns.

(For the sake of time/space, I'll omit the 3-part newspaper article.)

1. Make a table for the data.

2. Use the table to compare the costs of the items in the three towns.

3. WRITING Use the table from Exercise 1 and the table from Example 2 on page 9 to compare the wages and the costs of items in the three towns.

(Problems 4,5 have students reading from tables which are in the Lesson.)

COMPUTERS In Exercises 6-9, use the following information.

(Once again, I'll omit the newspaper-style article.)

6. Make a table of the data.

7. Which type of school owned the most CD-ROM computers?

8. In what year did the total number of schools that owned a CD-ROM computer more than double?

9. WRITING Write a short paragraph discussing other conclusions you can make from the data in the table from Exercise 6.

(Problem 10 has students reading a table printed in the Lesson.)

But wait! Remember students are supposed to describe in their MATH JOURNALS the reasoning they used at each step of the lesson! That would be MORE PAPER AND PENCIL.

Now to continue the assignment for Lesson 2 . . .

MATH JOURNAL
Suggest that students cut out tables from magazines and newspapers and paste them into their journals. Ask students to write questions that the tables can be used to answer.

This is classwork, folks. This is part of class time!

Where's the beef here? OK, I'll agree that that we want our students to be able to read and get information from a table. But how much of this lesson's time has been spent so far on reading and getting information from a table?

Where is 'the substance,the meat' in this lesson? Assuming this text is used in 6th grade, what concepts (from 5th grade) are being reviewed? What facts are practiced? What mental math activities? Oh, perhaps they were in the Warm-up Exercises! Let's look.

WARM-UP EXERCISES
Make a table to solve. Use a calculator.

More than one but fewer than 15 pencils were purchased at a total cost of $4.07. If each pencil was the same price, what was the price of one pencil?

Include the columns "number of pencils," "4.07/number of pencils," and "price of each pencil" in your table.

This exercise frustrates the teacher in me! For warm-up to this lesson, before reading and making a table has even been taught! But perhaps there will be more substance in the homework assignment . .

HOME INVOLVEMENT
Suggest that students work with family members and neighbors to gather data on sports-related topics. Some possibilities are: most popular sports, estimated number of hours in a year playing sports, estimated number of hours in a year watching sports, and so on. Urge students to organize their data into tables they can share with the class.

Note: No review of 5th grade concepts or drill of facts in Lesson 2. (There were none in Lesson 1.) That would use too much paper and pencil!

Perhaps in Lesson 3 ... No, that was the lesson on making lists which I wrote about in an earlier post. BUT Lesson 3 does have a Journal entry (more writing, more paper and pencil):

MATH JOURNAL
Have students record their thoughts about why lists are helpful. They may also include their work for Extra Example 2 in their journals.

Paper and pencil are well used here, yes, but ON WHAT? On students' writing their thoughts! Lists can be helpful; contributing thoughts orally on why lists are helpful can be useful. But using lesson time for writing these thoughts?

How many unsuspecting teachers think they are befriending their students by allowing them to spend class time on 'fun activities', when they are actually ROBBING THEM of precious time necessary for nailing down critical procedures and vital concepts needed later. It's also ROBBING THEM of future successes in more advanced mathematics. At the beginning of the year,teachers need to be reviewing and teaching procedures, teaching, teaching, teaching concepts, and practicing, practicing, practicing on those concepts and procedures.

Parents, you (probably)purchase most of the paper and pencils your students use. What do you want them to be used for?

I am hopeful that teachers will identify what skills and practices, what concepts and procedures are lacking and supplement these lessons.

Or will parents have to pick up the slack at home, or hire a tutor?

-- InterestedTeacher - 01 Jul 2005

Comments

Oh wait!

I think I messed up!

Do we now have two different pages on pencil and paper??

I think I linked to the wrong one--

-- CatherineJohnson - 02 Jul 2005

Oh, dear!!! I tried to change the names so they would be different.

-- InterestedTeacher - 02 Jul 2005

Don't worry--I got it fixed!

-- CatherineJohnson - 03 Jul 2005

MATH JOURNAL Suggest that students cut out tables from magazines and newspapers and paste them into their journals. Ask students to write questions that the tables can be used to answer. This is classwork, folks. This is part of class time!

Where's the beef here? OK, I'll agree that that we want our students to be able to read and get information from a table. But how much of this lesson's time has been spent so far on reading and getting information from a table?

Where is 'the substance,the meat' in this lesson? Assuming this text is used in 6th grade, what concepts (from 5th grade) are being reviewed? What facts are practiced? What mental math activities? Oh, perhaps they were in the Warm-up Exercises! Let's look.

This is utterly horrifying.

Always, always, always....simply looking at what's in these books is all you need to understand how back these curricula are.

-- CatherineJohnson - 03 Jul 2005

Learning math by writing about it is like learning to play baseball by writing about it.

-- BarryGarelick - 03 Jul 2005

What I didn't add to my post that was also in Lesson 2:

INTERDISCIPLINARY CONNECTION

Science Have students look in science texts and reference works to find tables that present interesting data.

Interdisciplinary connections are BIG in the eyes of all of our educators, and I don't dispute that there is great benefit in using time that can benefit two studies at one time. However, I'm still looking for some 'meat' and I see students looking through science texts. Looking through science texts.

Come on! A good teacher is smarter than this! Who can afford to waste more time by having the students look for tables? She/he will already have a table located in the science book. Or better yet, she will have a table on material related to the science study in progress or a study she is ready to begin. And she would save it until the science period begins.

But it's so much more fun for the students to be looking through the science book!!!!

Also not mentioned in my post was the clincher: Problem 11. It is Interdisciplinary Statistics, which gives project-related experience in gathering data and organizing it into table form. This project experience was begun before Lesson 1 and I'll cover that in my next post. Here is a preview:

MULTICULTURAL NOTE
A number of the world's most famous museums are known by a single name. Spain's Prado is home to a treasured collection of more than 2000 paintings by world-renowned artists. France's Louvre contains more than one million works, including major collections of Greek, Roman, Egyption, and Asian art. Russia's Hermitage, along with the neighboring Winder Palace, is the largest art museum in the world, with almost 3 million pieces housed in more than 13 miles of galleries.

I'll explain the ongoing project in my next page.

-- InterestedTeacher - 03 Jul 2005

Learning math like this is like driving through MacDonald^?'s and ordering a burger with no meat!!

-- InterestedTeacher - 03 Jul 2005

How about learning to fly a plane by writing about flying?
Or how would you parents like for your son's or daughter's driving ed instructor to teach them to drive by having them write their thoughts about driving?

I'm a teacher, but I'm a parent, also. We must demand more from those who design and write these textbooks from which our children will be preparing for their future. And maybe we need to demand more from those on schoolboards who adopt these textbooks.

My nextdoor neighbor just told me that she didn't know what her son, who just graduated from H.S., was going to do. She confided in me that his SAT scores weren't that good. She was a little upset with him. Perhaps it wasn't his fault!!

-- InterestedTeacher - 04 Jul 2005

And, all this writing is more difficult for some children than for others...

Let me ask, how many parents sitting at kitchen tables teaching mathematics are having their children write out paragraphs, about anything...? Private mathematics tutors spend (almost) no time making children "journal". Journaling about math.

-- BeckyC - 08 Jul 2005

BeckyC

Boy, you said it.

My neighbor and I were looking through some of the TRAILBLAZERS pages and they were just pure English Language Arts.

If you're a kid who struggles with reading, forget it.

Now you can be bad at reading and bad at math, too.

-- CatherineJohnson - 09 Jul 2005

Actually, that would be an interesting question.

Do private tutors EVER have kids journal about math?

I'd put money on it the answer is no.

-- CatherineJohnson - 09 Jul 2005

As a parent sitting at a dining room table right this second, with Christopher doing the mixed practice for Saxon 8/7 Lesson 13, I can tell you that the only journaling activity going on is the journaling I'm doing here, on ktm.

-- CatherineJohnson - 09 Jul 2005

In my state, the state math exam for grades 3-10 requires that the students expalin in writing why the student solved the problem as they did. The child could have an incorrect answer yet still have received points for a good written response....argh

-- LoneRanger - 09 Jul 2005

Didn't someone post a problem that had 40 points, of which only 2 were for the correct answer?

I think it was Barry, wasn't it?

Lone Ranger--did you see my post about outsmarting the test?

-- CatherineJohnson - 10 Jul 2005

No, I didn't. Where would I find it?

-- LoneRanger - 10 Jul 2005

I'll go find it.

-- CatherineJohnson - 10 Jul 2005

Here it is:

OutsmartingTheTests

One strategy my neighbor came up with is to have the child always write something, even if he doesn't have a clue what he's talking about.

Her son was scoring lower than his friend, because her son didn't write anything when he didn't know how to solve the problem.

His friend put something down--anything--and got some points.

-- CatherineJohnson - 10 Jul 2005

That would make a great page. All the various ways of getting around the "English" portion of the new-math standardized tests. That is very funny.

-- SusanS - 10 Jul 2005

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