Testimony to NJ State Board of Education
Dr. Janet H. Caldwell, June 17, 2009
I am Dr. Janet H. Caldwell, a professor of mathematics at Rowan University where I teach math
content courses. I have been recognized for my teaching as the Carnegie Foundation NJ
Professor of the Year and by the NJ Section of the Mathematical Association of America. I have
received awards from the NJ Association for Supervision and Curriculum Development and the
Association of Mathematics Teachers of New Jersey. I have served on national boards and
committees for three different national organizations.
New Jersey has made progress over the past decade in mathematics at the K-8 level. Our scores
on the National Assessment of Educational Progress (NAEP) have risen significantly to the
current levels. NJ is second among all of the states in grade 4 math and sixth at grade 8. Student
achievement has been steadily improving, an indication that we are on the right track. And while
New Jersey's mathematics standards are not solely responsible for this relatively high
performance, they are integral to it.
There are many benefits to be gained by developing and adopting national mathematics standards that
establish high expectations for all students in the United States. New Jersey's participation in this initiative
is welcome, for the national effort can only lead to high national mathematics standards if the states that
already have high state mathematics standards, like New Jersey, are active participants in the effort.
Our current standards were developed by looking at what other countries are doing in
mathematics; the current standards are "world class" and have been rated as among the best of
the states by Achieve, the organization playing a leadership role in developing the national
standards. They balance conceptual understanding, procedural skills, and problem solving.
Further, they provide a logical and psychologically appropriate sequence of topics from one
grade to another.
And yet, these standards can be better. They can be clearer, and they can and should be more
focused. At the invitation of the Department of Education, I served on its writing team, drafting
new, improved math standards. We completed our work in December.
The mathematics standards published in February by DOE were not based on our work. They
should not be used for any purpose. They do not build upon our current standards, they do not
reflect the recommendations of the NCTM Curriculum Focal Points nor of the National Math
Panel report. They are not internally consistent, they are not developmentally appropriate, and
they are less rigorous than our current standards. There are more than 200 indicators that have
changed grade levels, each of which will require new field testing of items for the state
assessments. This February draft is NOT a balanced approach to learning mathematics; it
-- - -
- --
focuses almost exclusively on skills. This draft was developed internally by DOE staff with
NO input from teachers and administrators. This draft is a sure path to lower math
achievement for NJ's students.
Since the publication of the February draft, DOE has convened a math task force which has met
four times but has made little if any progress in moving towards an acceptable draft of the math
standards. No further documents have been made available for review subsequent to these
meetings. It is not clear what path the revision of the math standards will take at this point.
Developing math standards is hard work. It requires extensive knowledge not only of
mathematics content but also of available curricula and of the psychology of learning
mathematics. It requires excellent writing skills and the ability to craft statements that are
mathematically correct, rigorous, and still clear to teachers and parents. It requires writers who
understand how to include basic skills without sacrificing the development of conceptual
understanding and problem solving. It also requires a very thick skin, since many will criticize
these standards without offering specific suggestions for improvement.
The NJ Math and Science Education Coalition convened a well-qualified standards development
group which reviewed the December 2008 and February 2009 versions of the standards, and
produced a document that seeks to
. incorporate the best recommendations of both versions,
· achieve a balance between the various perspectives on mathematics standards,
· achieve coherence across the standards and across the grade levels,
· be consistent with national recommendations, and
· maintain topics at the same grade levels as the current standards absent good reason to
change grade levels.
This document should be used as the starting point for New Jersey's next efforts. This
document should be used to evaluate any national mathematics standards that are proposed,
and it should be used to develop the next generation of state standards.
Two further points merit attention at this time.
1. High school students should be required to take mathematics each year that they are in
high school. Many students who fail basic skills math tests in college do so because they
took no math in their senior year and have forgotten much of what they once knew.
2. Elementary teachers need to be required to demonstrate their understanding of
mathematics. Presently, they are not required to pass any math test or take any
college-level math courses.
I thank you for your attention and your time and hope that my remarks have been helpful to
you in your deliberations. Should you wish to discuss any of these matters further, I would be
happy to do so.
The~
Nation's
NCES 2007-495NJ4
.
New Jersey
Ma t h em at I cs 2007
Grade 4
Report Card S tat e S nap S hot R e p 0 r t
Public Schools
The National Assessment of Educational Progress (NAEP) assesses mathematics in five content areas: number properties and operations; measurement;
geometry; data analysis and probability; and algebra. The NAEP mathematics scale ranges from 0 to 500.
Overall Mathematics Results for New'JerseY'~'.'illB_~~.n..
~....
, In 2007, the average scale score for fourth-grade students in New Jersey was 249.
This was higher than their average score in 2005 (244) and was higher than
.
New Jer&'Y (public)
1992a L.<,~R~
their average score in 1992 (227). t
1996a ~
2003
2005
2007
Nation (public)
2007
, New Jersey's average score (249) in 2007 was higher than that of the
nation's public schools (239).
Of the 52 states and other jurisdictions that participated in the 2007 fourth-grade
assessment, students' average scale score in New Jersey was higher than those
in 46 jurisdictions, not significantly different from those in 4 jurisdictions, and lower
than that in 1 jurisdiction.'
, The percentage of students in New Jersey who performed at or above the NAEP
Proficient level was 52 percent in 2007. This percentage was greater than that in
2005 (45 percent) and was greater than that in 1992 (25 percent).
, The percentage of students in New Jersey who performed at or above the NAEP
Basic level was 90 percent in 2007. This percentage was greater than that in 2005
(86 percent) and was greater than that in 1992 (68 percent).
.
A1('ag Score
I~
44'
22'
43'
42
22'
34'
40
~
I
!ms'
227
"
227'
239'
lID
244'
EI1II
249
112'
3'
38'
Percent below Basic Percent at Basic,
38 Proficlenl,
I and Advanced
42
oIProficient
II Advanced
33
ns
lli!I Below Basic 0 Basic 43
239
a Accommodations were not pennitted for this assessment.
NOTE: The NAEP grade 4 mathematics achievement levels correspond to the
following scale points: Below Basic, 213 or lower; Basic, 214-248; Proficient, 249281; Advanced, 282 or above.
Performance of NAEP Reporting Groups in New Jersey: 2007E.':":.i!'2.!!!',.'<'."'_"'_;.:',.-;j._: . ...... "" _'.' _ '..I#:'j:i3'i;jii;0:'!;jj::¥:(.(f;ki;:R;<;;iii§ji,'!i;#¥i\i.
Reporting groups
Male
Percent
Average
Percent
of students
score
below Basic
50
Female
2501
50
247
-
i
Percent of students at or above
Basic
10
90
11
t
Proficient
891
!
I
--_._j
I
25
2
I
79
h.
29
3
I
98
78
i
5
95
63
Black
14
232 j
22
78
Hispanic
20
234
21
2
500
J::
:t:
I
11
11
255
267
Advanced
49
57
, In 2007, maleIslander
students in New Jersey had an average score that was not
Asian/Pacific
8
i
551
White
Score I
Percent
i
Percentile
s
!
26
significantly different from that of female students. In 1992, there was no significant
differenceIndian/Alaska
between the average
American
Native score of male and female students. #
:t:
:t:
:t:
:t:
75th
270
~7
, In 2007, Black students had an average score that was lower than that of White
Eligible
for National School Lunch Program
29
233
78t
26
2
22
L
26
260
249' 249
students by 23 points. This performance gap was narrower than that of 1992 (38
.........
94
62
12
50t
69
255
6
250
260' h
points).
Not
eligible for National School Lunch Program
240
229' 229"
, In 2007, Hispanic students had an average score that was lower than that of White
~o
.........
25th
students
by 21 Score
points.
ThisBetween
performance
gap
was narrower
than
that of ........
1992 (32
- - ------------------------------------------------------ .----.- 230
Average
Gaps
Selected
Groups____
':. ../....
'.;'z.!¥!!....
D"""""'24s' :t:>
points).
220
207" 207'
241- ~2
.........
, In 2007, students who were eligible for free/reduced-price school lunch, a proxy for
210
1:1""""'227' ,~
poverty, had an average score that was lower than that of students who were not
200
220'
eligible for free/reduced-price school lunch by 22 points. This performance gap was
.. - - ........... Accommodations
were
not
permitted
narrower than that of 1996 (32 points).
o
D---C Accommodations were permitted
, In 2007, the score gap between students at the 75th percentile and students at the
'92
'96
'03
'05
'07
25th percentile was 36 points. This performance gap was narrower than that of
NOTE: Scores at selected percentiles on the NAEP mathematics scale indicate how well
1992 (41 points).
students at lower, middle, and higher levels performed.
~
i
I
I
I
# Rounds to zero.
" Significantly different from 2007.
~ Reporting standards not met.
t Significantly higher than 2005. 1 Significantly lower than 2005.
, Comparisons (higher/lower/narrower/wider/not different) are based on statistical tests. The .05 level was used for testing statistical significance. Statistical comparisons are calculated on the basis of unrounded scale
scores or percentages. Comparisons across jurisdictions and comparisons with the nation or within a jurisdiction across years may be affected by differences in exclusion rates for students with
disabilities (SD) and English language leamers (ELL). The exclusion rates for SD and ELL in New Jersey were 2 percent and 'percentage rounds to zero' in 2007, respectively.For
more intormation on NAEP significance testing see
hllc'lInces ed oovlnationsrecortcard/mathematics/interoret-results asc#statistical.
. Jurisdictions' refers to states and the District of Columbia and the Department of Defense Education Activity schools.
NOTE: Detail may not sum to totals because of rounding and because the 'Information not available' category for the National School Lunch Program, which provides free and reduced-price lunches, and the
'Unclassified' category for race/ethnicity are not displayed. Visit hllo'lInces ed oovlnationsrecortcard/statesl for additional results and detailed information.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various
.
years, 1992-2007 Mathematics Assessments.
----
i
The~
"'
M
Nation's
a
th
t
.
New Jersey
'
I
em a ICS 2007
GradeS
The
National
Assessment of Educational
Progress
geometry;
data
NCES
2007,;;,495NJ8"
Report Card
S tat(NAEP)
e S napassesses
S hot Rmathematics
e p 0 r t in five content areas: numberII properties and operations; measurement;Public
Schools
analysis and probability; and algebra. The NAEP mathematics scale ranges from 0 to 500.
Overall Mathematics Results for New Jersey~~'.'" "','-'"_",,,
",~",'&IR!I""'
" In 2007, the average scale score for eighth-grade students in New Jersey was 289. This was
higher than their average score in 2005 (284) and was higher than their average score
in 1990 (270).'
" New Jersey's average score (289) in 2007 was higher than that of the
nation's public schools (280).
" Of the 52 states and other jurisdictions that participated in the 2007 eighth-grade
assessment, students' average scale score in New Jersey was higher than those in 35
jurisdictions, not significantly different from those in 14 jurisdictions, and lower than
those in 2 jurisdictions.'
" The percentage of students in New Jersey who performed at or above the NAEP
Proficient level was 40 percent in 2007. This percentage was greater than that in
2005 (36 percent) and was greater than that in 1990 (21 percent).
" The percentage of students in New Jersey who performed at or above the NAEP
Basic level was 77 percent in 2007. This percentage was not significantly different
from that in 2005 (74 percent) and was greater than that in 1990 (58 percent).
Percentages at NAEP Achievement Levels and Average Score
New Jersey (pubUc
AV"',"age Score
j 1990a
37
1992a
2003
18"
270
"
272
"
281
"
284
"
1ii!13"
39
21"
38
27
38
27
113"
2005
2007
Nation (public)
2007
Percent below Basic Percent at Basic, Proficient, end Advanced
37
30
6"
IDII
289
ImiIII
o Proficient iii Advanced
[jJ Below Basic 0 Basic
39
I
_7
24
a Accommodations were not permitted for this
assessment
NOTE: The NAEP grade 8 mathematics achievement levels correspond to the
following scale points: Below Basic, 261 or lower; Basic, 262-298;
Proficient, 299-332; Advanced, 333 or above.
28
0
Performance' of NAEPReporting Groups in New Jersey': 2007.', -","'c:":""'.."Ji""Wh1"Wi"''''''','''''W''''"%irn,,.,Wt,,,,_1mi",;,Iii,',/!f,' 1'.i)"'"ffi."IIII",,'. ,',.1r""""",;;..""'.
Reporting groups
Male
Female
--------_._.__.__.-_.__.
White
Black
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Eligible for National School Lunch Program
Percent
of students
51
49
Average
Percent
score
below Basic
290
23
288 j
22
------_.
57
17
19
7
#
27
Percent of students at or above
B,asie
Proficient
77
43
78
38
Percent
Advanced
12
9
co
298
264
271
314
:j:
266
Not eligible for National School Lunch Program
71
297 j
"Average
In 2007,
male
students
in
New
Jersey
had
an
average
score
that
was
not
Score Gaps Between Selected Groups-..,='\' '.>'...'Y_'.':':.:1I!":,.v="'mii"::.'1'.W;
13
45
37
7
:j:
43
Score I
14.j,
87
55
63
93
:j:
57
51
14
20
69
:j:
17
--1'l
861
50
14
30 I
:j: i
2I
Percentile
Mathematics
Scores at Selcted Percentiles
500 J:
s
significantly different from that of female students. In 1990, there was no
significant difference between the average score of male and female
320
students.
7Sth
310
" In 2007, Black students had an average score that was lower than that of
~310
-:'4
294" 297"
300
White students by 35 points. In 1990, the average score for Black students
......
SOth
was lower than that of White students by 38 points.
290
291
284
286
" In 2007, Hispanic students had an average score that was lower than that
270" 274"
280
"
.......
of White students by 27 points. This performa'nce gap was narrower than
270
............... c 2Sth
that of 1990 (37 points).
~ 26261 26S
260
24S"
" In 2007, students who were eligible for free/reduced-price school lunch, a
2S8'
250 240248"
proxy for poverty, had an average score that was lower than that of
students who were not eligible for free/reduced-price school lunch by 31
. - - ............. Accommodations
were
not
points. In 2003, the average score for students who were eligible for
permitted
free/reduced-price school lunch was lower than the score of those not
c ------- CJ Accommodations were permitted
o
eligible by 34 points.
'03 '05 '07
'90 '92
" In 2007, the score gap between students at the 75th percentile and
NOTE: Scores at selected percentiles on the NAEP mathematics scale indicate how welt students
students at the 25th percentile was 49 points. In 1990, the score gap
at lower, middle, and higher levels performed.
between students at the 75th percentile and students at the 25th percentile
was 49 points.
# Rounds to zero.
~ Reporting standards not met.
~
.
...a
" Significantly different from 2007.
1 Significantly higher than 2005.
L Significantly lower than 200S.
, Comparisons (higherllower/narrower/wider/not different) are based on statistical tests. The .OS level was used for testing statistical significance. Statistical comparisons are calculated on the basis of
unrounded scale scores or percentages. Comparisons across jurisdictions and comparisons with the nation or within a jurisdiction across years may be affected by differences in
exclusion rates for students with disabilities (SO) and English language learners (ELL). The exclusion rates for SO and ELL in New Jersey were 3 percent and 1 percent in 2007,
respectively. For more intormation on NAEP significance testing see
h1l0'lInces ed oov/nationsreoortcard/mathematicslinteroret,results aSD#statistical.
, . Jurisdictions' refers to states and the District of Columbia and the Department of Defense Education Activity schools.
NOTE: Detail may not sum to totals because of rounding and because the 'Information not available' category for the National School Lunch Program, which provides free and reduced-price lunches, and the
"Unclassified" category for race/ethnicity are not displayed. Visit h1lD'/inces ed oov/nationsreDortcard/statesl for additional results and detailed information.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1990-2007
Mathematics Assessments.
535 teachers respond to Feb 2009 NJDOE written Math Standards
1. Rigor
The content is cognitively demanding for the grade/grade level cluster
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
5%
13.0%
28.2%
16.4%
37%
and CPls reflect higher levels of Bloom's Taxonomy or Norman Webb's
Depth of Knowledge.
2. Rigor
The standards/CPls represent the content and cognitive demand necessary
for students to succeed in credit-bearing college courses without
remediation, in other postsecondary education and training and quality
high-growth careers.
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
8.1%
20.1%
8.3%
15.9%
37.7%
3. Relevance/Real World Applications
The standards/CPls sufficiently focus on the content and skills needed
for transfer to ever changing real world situations.
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
4.8%
22.5%
9.4%
19.3%
43.4%
4. Relevance/Global Perspectives
The standards/CPls represent content and skills that foster analysis of
global perspectives and global dynamics.
Strongly
Agree
2.9%
Agree
Neutral
Disagree
17.4%
18.3%
17.8%
Strongly
Disagree
41.1%
5. Coherence/Progression
Content and CPls systematically increase in complexity across
grades/ grade level clusters.
Strongly
Agree
10.3%
Agree
Neutral
Disagree
25.3%
11.0%
15.9%
Strongly
Disagree
37.3%
6. Focus
Standards/CPls establish priorities about content and skills to be
acquired.
Strongly
I Agree
I Neutral
I Disagree
Strongly
I
---
-.- -- --- --
Agree
5.8%
22.7%
11.7%
Disagree
41.6%
18.3%
7. Focus
Content and skills are manageable at each grade / grade level cluster.
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
8.1%
20.1%
8.3%
15.9%
37.7%
8. Specificity
Standards/CPls are an appropriate "grain size" - specific enough to
develop and guide curriculum, but broad enough to capture "big ideas"
and to allow for a variety of curricular approaches.
Strongly
Agree
7.0%
Agree
Neutral
Disagree
28.3%
9.3%
19.0%
Strongly
Disagree
36.4%
9. Specificity
CPls provide sufficient detail to convey the level of performance expected
and may be assessed using multiple measures (e.g., state test, performancebased tasks, project-based learning, teacher observations).
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
6.2%
28.0%
10.6%
16.4%
38.8%
10. Measurability
CPls focus on results by using performance verbs that ask students to
demonstrate knowledge and skills (e.g., compare, explain, analyze)
rather than process verbs (e.g., understand, appreciate, examine).
Strongly
Agree
Neutral
Disagree
Strongly
Agree
Disagree
7.2%
33.6%
10.7%
14.4%
34.2%
11 . Clarity
Standards/CPls are communicated in a language that is clear and
understandable.
Strongly
Agree
8.5%
Agree
Neutral
Disagree
28.5%
13.7%
15.2%
Strongly
Disagree
33.9%
- -
-- --- -
December version
February version
Comments
Recommended Indicators
Numerical operations are used to
model quantifiable real-world
situations.
Fluency in computation is essential as
numerical operations are used to
model quantifiable authentic
Change first sentence of February
version as in grade 3.
Computational fluency involves using
efficient and accurate methods for
computing that are based on well-
.
Addition and subtraction of
situations.
understood properties and number
decimals, fractions, and/or
mixed
.
Addition and subtraction of
relationships. At this grade level, the
numbers
decimals, fractions, and mixed
focus should be on:
Division of a 3-digit number
by a
numbers
.
Standard 4.1 - Number and Numerical Operations, Strand B: Numerical Operations - Grade 5 - March 23, 2009
.
2-digit number representing
remainders as fractions
.
Addition and subtraction of
Division of a 3-digit number by a
decimals, fractions, and mixed
2-digit number representing
numbers
.
remainders as fractions
Division of a 3-digit number by a
2-digit number representing
remainders asfractions
1. Use appropriate arithmetic
operations in problem situations.
.
Whole numbers
- all four basic
operations
.
Decimals, fractions, and/or mixed
numbers - addition and
subtraction
2. Construct, use, and explain
B2. Add and subtract fractions
B2. Do not need to specify that the
procedures (pencil-and-paper or
(including mixed numbers) with
mental math) for performing addition
and subtraction with fractions, mixed
numbers, and decimals.
different denominators.
denominators need to be different
that is understood.
B3. Use models to show an
B3. This has not been in Grade 5
understanding of multiplication and
although most teachers start this
division of fractions.
towards the end of the year
-
BB2. Use and explain efficient and
accurate procedures (modeling, paper
& pencil, estimation, and mental
math) to add and subtract fractions
and mixed numbers.
- there is
so much in Grade 5, though, that this
should be omitted and place in Grade
6, as recommended in CFP.
B4. Multiply and divide fractions to
B4. This should also be postponed to
solve problems.
grade 6 as recommended by CFP there is too much in grade 5 and this
10
3.Use an efficient and accurate pencilandpaper procedure for division of a 3-digit
number by a 2-digit number.
Represent remainders as fractions
.
fractions should be expected at this
grade level, as in indicator BB3.
people ate l/3, 1/4, and 1/5 of a pie,
what portion of the pie remains?)
B5. Add and subtract decimals and
estimate to verify the reasonableness of
the results.
B5. Broaden this to include mental
math.
BB4. Use and explain efficiellt and
accurate procedures (modeling, paper &
pencil, estimation, and mental math) to add
and subtract decimals.
B I. Solve problems involving
multiplication and division of any
whole numbers.
B I. "Any whole numbers" is too
broad - we don't want every student
to have to be able to multiply 4 digits
by 5 digits or divide 8 digits by 2
digits.
BBl. Use and explain efficient and accurate
procedures (modeling, paper & pencil or
mental math) to divide numbers up to 1000
by numbers less than 100, representing
remainders as
fractions.
The "multiplication" part of B 1 is
addressed in indicator BB3 at Grade
4.
The "problem solving" part of B 1 is
addressed in indicator BB3.
At each grade level, as students learn
new operations or apply them to new
numbers, they should be learning about
how those operations might best be
applied. BB7 here is parallel to BB5 at
Grade 3.
4. Select and apply the appropriate
method of computation from among
pencil-and-paper, mental math, or use of a
calculator or computer to solve real world
problems.
Not needed
5. Add or subtract fractions and decimals
using estimation strategies. 6. Determine
whether a given estimate is an
overestimate or an underestimate.
7. Determine the reasonableness of an
answer by estimating the result of
operations.
BB7. Select and use appropriate
computational methods (e.g., estimation,
mental math, calculators, or pencil-andpaper) to solve problems involving all
operations on whole numbers. and addition
and subtraction of fractions, depending on
the context and numbers involved.
This indicator should be included.
BB5. Determine whether a given
estimate is an overestimate or an
underestimate.
B6. Use estimation to decide whether
answers are reasonable in addition,
subtraction, multiplication and division
problems.
B6. This is too limited - want
students to use estimation with
fractions & decimals too.
BB6. Use estimation to decide whether
answers are reasonable in problems
involving computations with whole
numbers, and addition and subtraction of
decimals and fractions.
B7. Use mental arithmetic to add or
subtract simple decimals.
B7. This is included in indicator BB4.
11