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Improving a Curriculum
1. Create big ideas if a packaged curriculum or textbook does not have them.
a. In elementary math, teach the number line.
_____________|_______________
-5 –4 –3 –2- 1- 0 +1 +2 +3 +4 +5
Also, teach that the 4 operations are all versions of counting--forward and
backward, by ones and by groups of ones.
b. In history, (1) the concept of freedom; (2) the model/theory that all social
arrangements (social class relations, economic systems, religious systems, family
systems) are combinations of ideas (concepts, values) and technologies (ways of
doing things); (3) the model/theory that societal problems (over resources,
conflict, power) lead to solutions and that solutions have consequences (desirable
and undesirable).
2. Create strands if a curriculum or text does not have them. For example,
a. In beginning reading, add a strand (brief tasks in 100 lessons) on explicit phonics
instruction (sound/symbol  sounding out words).
b. In any subject, teach comprehension of text (e.g., a progression of questions:
repeat sentence, who did…, what happened…, why do you think…, think of
another thing that…what figures of speech…)
c. Vocabulary. New ones every day. Review. Use in sentences.
3. Add/insert units if a curriculum or text makes too large a jump.
a. Algebra. Before going on to new material, ask yourself, "How well can
they…?" Then give a practice set on generalization (different examples of the
same problem/strategy type) and discrimination (distinguish between similarlooking examples of different types), or on retention.
(a + b)(c + d) (a + b)(c - d) (a - b)(c + d) (a - b)(c d) (a x b)(c + d) etc.
2(a + b)(c + d) etc.
b. Any subject. Ask, "Do they need a few more?" Add more problems to an
acquisition set to ensure firm knowledge and/or to cover a wide enough range of
examples.
c. Juxtapose examples and nonexamples to ensure that students get essential vs.
irrelevant samenesses and differences.
(1) Model (of how to use the verbal definition to identify granite/not granite, after
stating verbal the definition)
"This is granite. This is granite. This is granite. This is not granite. This is
not granite. This is granite." [Then immediately give an…]
Acquisition test. "Is this granite?" Yes. "How do you know? " (Use both
examples and nonexamples. Correct all errors. "This is not granite. It does
not have mica. Is this granite? " (use the same example or nonexample).
(2) Model: "This is a linear function.
This is a linear function.
different slopes)
It is a straight line.
It is a straight line. (Give more examples,
This is NOT a linear function.
more examples, linear and not linear.)
It is NOT a straight line. " (Give
Acquisition test: "Is this a linear function?
know?…
Is this a linear function?
Yes. How do you
No. How do you know? " [More.]
(3) "This (point) is aaa. This (point) is NOT aaa." [More.]
(4) "This parentheses is squared. So (rule). We add the two terms inside and
then square the sum. This parenthesis is NOT squared. So, we just add the
two terms inside." [Model the operation.] "Here I go…" [Then continue with
more examples.] "Is this parenthesis squared? " Yes. "Yes, it is squared. So,
what do we do? " We add the two terms inside and then square the sum.
"Yes, do it… Is this parenthesis squared? " No. "No, it is not squared. So,
what do we do? " We just add the two terms inside. "Yes, do it…"
d. A unit on a theory (big idea) of revolution before students read about a particular
revolution.
e. A review unit on multiplication before students begin division.
4. Add strategic integration within and/or across lessons.
a. After they learn a little about rhyme schemes, symbolism, and figures of speech,
students write poems.
b. After they learn about wars (democratic armies, mercenary armies, coerced
armies; wars of conquest, wars of defense; effects of different technologies and
styles of combat), students predict the sequence and outcomes of war with
Islamofascism.
c. After the have learned a few letter-sound correspondences, students learn the
sounding out strategy for words.
5. Rearrange the sequence of tasks within a lesson or across lessons if the sequence
is not a faultless logical progression.
a. Teach the definition of mitosis before naming the phases. (A text may have it
backwards.)
b. Have students first skim the running vocabulary that they will next use to
translate a simple passage in a foreign language.
c. At the beginning of foreign language instruction, have students use a running
vocabulary to translate a simple passage in a foreign language. Immediately
afterward (and after they have compared their translation with an accurate model,
and revised accordingly) give them a few grammar rules about a few examples in
the passage; e.g., that the definite article in Greek changes depending on the case
and number of the noun. (Instead of giving a lot of abstract grammar rules
first!)
"Notice the different forms of the definite article…"
Singular
Nominative
o
Accusative
ton
Plural
to oi
h
thn
to
"Notice the change in verb ending between bainei
(line 4)
touj
ai
taj
ta
ta
(line 2) and eisbainousin
bainei is third person singular (he, she, it goes)
bainousin is third person plural (they go)." [In other words, you are not teaching
the whole conjugation, just two endings.]
[Future passage translations would have the rest of the verb endings. Then you would
review all, and put them in the usual format, as a summary of the examples.]
Conjugating regular present tense
Singular
First
bainw
Plural
bainomen
eij bainete
Second bain
Third

bainei
