1. Slide1:
 My name is Hailey Evans and my thesis mentor, Professor Stokes, and I have been workingon a project
entitled: DoingmorethanCommonCore(Mathematics inKindergarten,FirstGrade,andSecondGrade)
Slide2:
 The Common Core is a set of learning trajectories that children should master before advancing to the next
grade level. It claims to be based on research related to the developing brain, yet underestimates the potential
of young grade school students.
 This is evidenced by American vs.East Asian student performance. East Asian students score significantly
higher in numerical tasks than do American students of the same age.
 Furthermore, the Common Core standardizes expectations withoutstandardizing curricula. There is little
consistency in the way mathematics is taught across classrooms.
Slide3:
 There are problems with the way mathematics is taught in American grade school classrooms, which is a result
of the lackof standardization in curricula.
 Educators teach withmaterial instead of mathematic complexity,which leads to cognitiveoverload in students.
 In grade school classrooms, there are too many manipulatives and not enough learning. Manipulatives are
teaching aids, such as counters, sticks, cubes, and blocks.
 Children learn how to use manipulates without understanding the concepts behind them. They think of five
blocks, fivecounters, fivesticks, and fivecubes as separate entities, rather than associating all of them with the
number five.
Slide4:
 We would like to propose a solution: a curriculum that makes math more simple and less abstract, such as Only
TheNUMBERSCount,developed by Stokes and colleagues
Slide5:
 How does Only TheNUMBERSCountmake math more simple?
 It uses one manipulative: “blocks” that can be used tangibly or drawn on a chalkboard, a white board, or a
SmartBoard©, or paper. This is the most basic version of the count and combine chart, whichstudents are
introduced to in kindergarten. They read each line as “number 1, same as, wordone, equals one block”.This
helps clarify that numbers are numbers, whether they are represented by symbols, words, or objects.
 These blockscome in differentcolors for differentoperations (green for addition, multiplication, and division
and red for subtraction). They manipulate these blockswith their hands to make math sentences, or, as wecall
them, combinations.
 Furthermore, blocksare easily translatable to wordproblems. We just tell our students to think of the objects
in the problem as blocks.

2. Slide6:
 How does Only the NUMBERSCount make math less abstract?
 It uses a ten-based count,inspired by the counts of East-Asian languages, that is shown to your right. This count
gives numbers meaning. “Eleven” is abstract. “Ten-one” has clear and obviousmeaning. It’s a ten and a one.
 Placevalue is built into the count. Here is a later version of the count and combine chart that students use later
in kindergarten and first grade. They know that ten-one is the same is one ten blockand one one block.Of
course, they also know that it is the same as eleven one blocks.But, this makes it so that place-value is not a
foreign concept.
 This count also makes double digit addition and subtraction much easier, because our students know to add or
subtract the tens, then add or subtract the ones.
Slide7:
 So, what are our research questions?
 We already know that kindergarteners and first graders taught with Onlythe NUMBERSCount© master the
concepts taught in this curriculum, as measured by pre- and post- tests we wroteand administered
 Our questions now are, 1. Doesthissuccesstranslateto the expectationslaidoutbythe CommonCore?In other
words,howdo studentstaughtwith thiscurriculum performonstateexaminations? and 2. Do secondgraders
taughtwith this curriculum continueto improve?
Slide8:
 Our study employed a longitudinal research design. We looked at three classrooms over three years
(kindergarten, first grade, and second grade)
 Our students are of mixed race and socioeconomic status from a suburban public school in Lodi, New Jersey.
 We looked at students’ performance on state testing, since this should be indicative of their performance in
parallel with the expectations of the common core
 In Kindergarten, New Jersey uses Early Numeracy testing 2 times per year, whichassesses basic skills like oral
counting, number identification, quantity discrimination (whichis identifying a number as larger or smaller
relative to another), and missing number (such as in a series, like 14, 15, blank). It is scored as a percent, from
1-100.
 In 1st and 2nd grade, Renaissance Star Testing is used in New Jersey 3 times per year to lookat common core
competency.It is scored as grade.month (forexample, a score of 2.3 wouldbe given to a student who scored at
a 2nd grade, 3rd month level).
 ProfessorStokes and her laboratory assistants also observed the classrooms weekly to ensure the curriculum
was taught consistently across classrooms and to trackthe progress of individuals and classrooms.
 We also provided weekly instruction by modeling lessons forthe teachers torepeat and build upon.
Slide9:
 Here is a summary of our results as average scores and percentiles for each state test (kindergarten fall,
kindergarten spring, 1st grade fall, 1st grade spring, 2nd grade fall,and 2nd grade winter). The take away message
here is that our students consistently scored above the 50th percentile, whichcan be taken as the average for
the typical New Jersey student. By the middle of second grade, they are, on average, scoring at a level indicative
of the end of second grade.

3. Slide10:
 This is just a graphical representation showing that from the beginning to the end of kindergarten, our
students’ Early Numeracy scores significantly improved.
Slide11:
 Here on the left you have average Renaissance Star scores in 1st grade (in light blue) and 2nd grade (in dark
blue). Our students began first grade scoring at mid-1st grade level and were scoring at an end-of-2nd-grade
level by the middle of second grade.
 Percentiles are on the right and show that our students consistently score aboveaverage, marked by the 50th
percentile in red.
Slide12:
 Since there were such large standard deviations, as expected due to vast individual differences, I chose to select
a representative student fromeach of 3 different groups.
 Honors students were chosen by their teachers to complete an enrichment class in the spring of 1st grade. As
you can see, they were scoring at close-to 5th grade levels by the middle of second grade
 Standard students were identified by their teachers as individuals whoshowed typical performance. They were
still scoring at later-2nd grade levels by the middle of second grade.
 In our data set, wehad 5 English-language learners who spoke exclusively Spanish at home. They were initially
struggling but soon achieved at a similar level to their English-speaking classmates.
Slide13:
 I also chose tolook at differences in achievement between males and females. As you can see, there was only
one significant difference,with males scoring higher than females during the 2nd grade winter examination.
Slide14:
 Because the average student taught using Onlythe NUMBERSCount© scores abovetheir grade level and above
the fiftieth percentile, this curriculum seems to allow students to exceed Common Core standards
 This suggests that revisions to the Common Core can, and should, be made so that children can reach their
fullest potential.
Slide15:
 Suggested common corerevisions are as follows:
 Firstly, introduce place-value as early as possible by integrating this concept into a base-10 count. The
additional amount of time necessary to teach a base-10 countalongside the English countis trivial compared to
the payoff.
 Secondly, standardize curricula to include a single manipulative. This manipulative should be easily
translatable to word problems and should be both tangible and transferable toa multitude of surfaces
(chalkboard,white board, SmartBoard©, paper, etc.)
 Thirdly, the common core should recognize what the developing brain is capable of. This includes: subtraction,
double-digit addition, and place-value in kindergarten; double-digit subtraction and multiplication in first
grade; and division and fractionsin second grade. This may allow us to take advantage of neural plasticity–
math may be much like learning a language. If there is a mathematical sensitive period, it is essential to
introduce complex concepts early!

4. Slide16:
 There were several limitations to the present study. Firstly, the small sample size and the availability of
demographic information limited our ability to reasonably look at differences in race, socioeconomic status,
and home environment. Therefore, there are large standard deviations in our data due to immense individual
differences.
 Additionally, the longitudinal nature of the study made it difficultto accommodate forstudents whomoved and
transferred schools. It also mandated that we exclude students whowere held backa grade.
 Due to ethics, it was not possible to look at students who receivea standard curriculum versus Only the
NUMBERSCount© while controlling for other variables, such as school, teacher, etc. Much like in
pharmaceutical research, once we discovered how well this curriculum worked,it would have been unethical
to withhold it from some students and give it to others
Slide17:
 I’d like to briefly address the noted gender differences.
 Other studies continually show no difference between male and female performance in elementary
mathematics.
 But, some research has indicated heightened male performance in complex mathematical problem solving (not
until high school)
 Our data only shows a significant difference between males and females at the most recent examination
(winter of second grade)
 This may reflect the fact that complex problems are being introduced sooner with Only the NUMBERSCount© .
 However,further data must be collected before this idea can be further investigated, because we only saw a
difference at one testing point.
Slide18:
 Moving forward,we’d like to continue monitoring students in this longitudinal study using both state tests and
the pre- and post- tests developed for Only theNUMBERSCount©. This will help us assess whether or not
gender differences in performance arise in higher-level mathematical problem solving
 Perhaps we’d like to extend Only theNUMBERSCount© beyondearly elementary school. However,the
curriculum may have lasting effects,even if it is only taught in early elementary school,because it changes the
way children think about numerical patterns. Observational data shows that students whoreceive this
curriculum in early elementary school continue to achieve highly throughout elementary school.
 If we extend the curriculum,we’d adapt the fundamental base-10 count and single manipulative to encompass
concepts such as exponents and roots, algebra, geometry, trigonometry, and eventually calculus. Wewould
have to seek expert advice, because the curriculum was developed by non-experts.
 We would definitely like to introduce the curriculum to other schools.