Last Modified:
Thursday, 11-Jan-2001 16:03:29 EST
Curriculum Projects
This project is designed to help you get a feeling for what some
elementary mathematics textbooks look like, to familiarize you with
"scope and sequence charts" and to get you thinking about where new
material is introduced in the curriculum.
Background Reading
Before beginning the project you must read the article
"How Much of the Content in Mathematics Textbooks is New?" by
J.R. Flanders (to be distributed in class) and pages 497-499 of
Van de Walle.
Assigned Texts
In order to prevent some of the competition for books and also to
gave the class (and each group) see a variety of texts, I will assign
you textbook series and grade levels to use.
The textbooks available in the curriculum center include the following
-
Mathematics in Action,
MacMillan, 1991.
QA 107 M3835 1991.
-
Mathematics: Exploring your world,
Silver Burdett, 1992.
QA 135.5 M3848 1992.
-
Exploring Mathematics,
Scott Foresman, 1996.
QA 107 E97 1996.
-
Math in My World,
McGraw-Hill, 1998.
QA 107 M258 1998.
-
Math Central,
Houghton-Mifflin, 1999.
QA 107 H67 1999.
Use your card and the table below to determine your assigned textbook
series. The letter indicates the series, the number indicates the
grade level.
| *
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
|
| Red
| A3
| B3
| C3
| D3
| E3
| A4
| B4
| C4
|
| Black
| D4
| E4
| A5
| B5
| C5
| D5
| E5
| free choice
|
Report
Work in pairs for this project.
Your partner is the person sitting at your table (same color
and number card as you).
-
Write a brief summary of Flanders' article. What was he main point
and how did he try to demonstrate it?
-
In the textbooks you are considering, what percentage is "new"? Be sure
to explain how you arrived at these figures. Important notes:
- You do not need to use Flanders' page by page method.
In particular, you may find that using a scope and sequence chart will
greatly simplify this task.
-
You will need to look at previous books in the series to tell if
topics are new or not.
You should prepare one type-written report for the two of you.
The gaol of this project is to help you see how different types of
problems appear in elementary math texts.
You will do this by looking finding problems of certain types from
each of TWO different textbooks.
You may work in pairs for this project.
This time you may choose your own partner.
Use the same textbook for this project that one of you used for curriculum
project 1 plus one assigned to one of you in the chart below.
Use the same grade level in both textbook series.
-
Investigations in Number, Data, and Space,
TERC - Dale Seymour Publications, 1998.
QA135.5 I58 1998.
-
Math Trailblazers,
University of Illinois -- Chicago and
Kent/Hunt Publishing Co., 1998.
QA 135.5 .K41 1998.
-
Everyday Mathematics,
Everyday Learning Corporation, 1992 and 1998.
QA 135.5 .B472 1992, QA 135.5 .B473 1998.
| *
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
|
| Red
| A
| B
| C
| A
| B
| C
| A
| B
|
| Black
| C
| A
| B
| C
| A
| B
| C
| A
|
Report
On pages 48-50, Van de Walle lists 9 types of problems that he claims
"occur across most grade levels and content strands".
In each of your two texts
(one from the project 1 list and one from the project 2 list),
find seven different problems that are examples of seven of these types.
(That's 14 problems total.)
For each problem
-
write down the problem,
-
record its location (series, grade level, page),
-
identify its type, and
-
explain
why you have categorized it the way you have.
(Note: some problems fall into more than one category.)
Your report should be type-written (although you may supplement with
hand-drawn pictures, etc, if needed). Be sure to include the information
regarding which textbook(s) you used for the project.
You may work in pairs for this project. Whether you
work in pairs or alone, you will need to look at TWO
textbook series (and probably more than one book from each series).
The goal is to find out when and how the arithmetic operations
(addition, subtraction, multiplication and division)
and algorithms are introduced in these two texts.
For the first, choose
the series that one of you was assigned in project 1.
For the second, use the chart below to determine which
of the following texts to use:
-
Investigations in Number, Data, and Space,
TERC - Dale Seymour Publications, 1998.
QA135.5 I58 1998.
-
Math Trailblazers,
University of Illinois -- Chicago and
Kent/Hunt Publishing Co., 1998.
QA 135.5 .K41 1998.
-
Everyday Mathematics,
Everyday Learning Corporation, 1992 and 1998.
QA 135.5 .B472 1992, QA 135.5 .B473 1998.
| *
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
|
| Red
| A
| B
| C
| A
| B
| C
| A
| B
|
| Black
| C
| A
| B
| C
| A
| B
| C
| A
|
Report
In each of the following, when asked to locate something, report
the page, chapter, grade level and book (if the series has
more than one book per grade level).
Also estimate where approximately this topic falls in the school year
(first quarter, second quarter, etc.) The scope
and sequence chart will be useful for this, especially when there
are several books involved.
Do this for each of the
two textbook series you have been assigned. (Clearly label which
is which.)
-
Addition.
Find out where in your series the addition algorithm for the sum of two
2-digit numbers is introduced.
Do problems that involve regrouping occur along with those that do not?
If not, locate where problems requiring regrouping first appear.
What conceptual rationale is provided for the algorithm in each case?
-
Multiplication.
Where is the multiplication algorithm first introduced?
(This will probably involve the product of a 1-digit number with
a 2-digit number.)
What conceptual rationale is given for the algorithm (repeated addition,
array, something else, none at all)?
Where does the product of two 2-digit numbers first appear?
Does your textbook make use of an "intermediate algorithm" before moving
to the "standard algorithm"?
Support your answers with relevant examples and citations.
-
Division.
- Meaning.
Find the place in your textbook series where the meaning of division
is introduced. Is division first introduced in terms of "repeated subtraction"
or "fair share" or are both illustrated right away? Give the initial examples
used and justify your classification as "repeated subtraction" or
"fair share".
- Algorithm.
Where is the division algorithm introduced? (This will probably involve
1-digit divisors.)
What conceptual basis is provided to motivate or justify the procedure?
Do any of the examples or exercises in this first lesson involve remainders?
If not, where are remainders introduced? Support your answers with
the relevant examples and citations.
Finally, give a quick comparison of the two textbook series. Do they do
things similarly and at similar times or quite differently or at
quite different times.
You may work in pairs for this project. Whether you
work in pairs or alone, you will need to look at TWO
textbook series.
The goal is to find out when and how division of fractions is
explained.
For the first textbook series, choose
the series that one of you was assigned in project 1.
For the second, use the charts from project 3 to determine which
texts to use.
Report
In each textbook series, find the grade level where division of
fractions is introduced for the first time.
Where does this lesson occur? (Give the book(s), page, and chapter
references as well the approximate location in the year --
first quarter, second quarter, etc. Note that for some texts
this "unit" might be presented in several of the books at roughly
the same time, be sure to explain this. Consult scope and sequence
charts to help you locate things.)
How is "invert-and-multiply" explained, or is it simply presented as
a "rule"? Are any other algorithms for dividing fractions presented?
In what order?