A. Project Rationale Teaching second grade ELL...

Course: TED 5300 Instructor: Dr. Pei-Ling Hsu

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Template 04

Project Report (Minimum: 3000 words)

Name: Maura L Loya

Student ID: 80465421

A. Project Rationale

1. Project title. Teaching second grade ELL students base-ten two-digit addition and

subtraction.

2. Problems and the importance of the project. Teachers of English Language Learners

(ELLs) need to accomplish two goals related to their students and math content, which

are: math conceptual understanding and proficiency in English language. In order to

accomplish the goals, teachers should consider a variety of instructional strategies that

support ELLs. All learners need to clarify their developing understanding, test

hypotheses, and feedback about their thinking. These activities are conducted through

language. When a learner is carrying out all of this cognitive work in a second language,

limitations in language can lead to limitations in learning (Bresser, Felux & Melanese,

2009). Some students struggle with math but for some others it comes naturally. Thus, it

is important to provide students, but especially ELL students, with opportunities to speak,

read, and listen in a mathematics class with the appropriate scaffolding. It is important to

make sure that students understand math vocabulary and that they have opportunities to

use it. Skills like solving word problems, following instructions, understanding and using

mathematical vocabulary correctly a language proficiency that sometimes exceeds our

expectations. We tend to think of mathematics as a subject that does not require a strong

command of language. In reality, however, mathematical reasoning and problem solving

are closely linked to language and rely upon a firm understanding of basic math

vocabulary (Jarret, 1999). For many educators, the challenge of bringing language and

math instruction together is a relatively new one, and many math teachers who do not see

themselves as language instructors are now responsible for providing effective math

instruction to ELLs (Bresser et. al., 2009) More than a half of this particular group of

ELL second-grade students failed their math benchmarks topics 1-4 (see appendix 1),

which included addition, subtraction, expanded form, number line, patterns, greater than,

smaller than and equal to, number arrangement from bigger to small and vice versa. The

importance of the project was to find if by using manipulative materials students were

able to hold and move on their own (Shaw, 2002). Numbers and operations in base ten

is one of the focal domains in each grade from kinder through fifth grade. Even with this

strong focus on numbers throughout the K–12 curriculum, experience considerable

difficulty constructing appropriate number concepts of multi-digit numeration and

appropriate procedures for multi-digit arithmetic. Children often learn standard

algorithms (procedural understanding), rather than developing number concepts and

strategies (conceptual understanding). Thus, they tend to view single digits as linked

together, instead of numbers of ones, tens and hundreds (Thanheiser, 2012). Parrish


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(2014) mentioned that according to Fennel and Landis, number sense is an “awareness

and understanding about what numbers are, their relationships, their magnitude, the

relative effect of operating on numbers, and the use of mental math and estimation” (p.

36). By looking at numbers as whole quantities instead of concatenated digits, students

would have a better understanding of place value, and “right” problems should be used to

build mathematical understanding and knowledge (Parrish, 2014). A deep understanding

of mathematics involves understanding how numbers work without memorizing facts

fixed in the base-ten system. For example, 2 + 2 = 4 can be seen as 4 things that can be

broken into two equal groups of two. This study attempted to teach addition and

subtraction together within the base-ten system by teaching numbers as tens and some

ones, and by using place value as a tool to teach addition and subtraction. It is worth

mentioning that or this purpose, mastery of place value and number line was necessary to

understand basic math concepts to regroup. By starting with manipulatives (counting

bears, base-ten blocks or counting tiles) students, regardless of language skills, were able

to find patterns in numbers. In so doing, ELLs built a concrete understanding of the

taught math concept. Addition and subtraction using one digit, fact families (3 + 4 = 7, 4

+ 3 = 7, 7 – 4 = 3, 7 – 3 = 4) and missing addends created the base towards addition and

subtraction of two digit numbers. By taking into consideration the theoretical framework:

How did the use of alternative teaching methods like manipulatives and paired work

improve student engagement and understanding of the underlying concept of addition and

subtraction?

3. Project objectives

• Understanding of the basic addition and subtraction concepts

• Understanding of place value

• Regrouping in addition and regrouping in subtraction.

• Make the transition from simple addition and subtraction into regrouping with 2

digit numbers.

4. TEKS Alignment

§111.4. Grade 2, Adopted 2012.

(a) (4) (A) Students develop an understanding of the base-10 place value system and

place value concepts. The students' understanding of base-10 place value includes ideas

of counting in units and multiples of thousands, hundreds, tens, and ones and a grasp of

number relationships, which students demonstrate in a variety of ways.

(a) (4) (B) Students identify situations in which addition and subtraction are useful to

solve problems. Students develop a variety of strategies to use efficient, accurate, and

generalizable methods to add and subtract multi-digit whole numbers.

(a) (4) (C) Students use the relationship between skip counting and equal groups of

objects to represent the addition or subtraction of equivalent sets, which builds a strong

foundation for multiplication and division.


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htpp://ritter.tea.state.tx.us/rules/tac/chapter111/ch111a.html

B. Project Design

1. Collaborator(s) second grade teacher Mrs. Schoenbrun. She is a bilingual second-grade

teacher at Beall Elementary school in central El Paso. Mrs. Schoenbrun agreed to

participate in the study seeking to help students improve their addition and subtraction

skills. Whenever the participants of the study were pulled out of their regular routine to

receive the designed interventions, Mrs. Schoenbrun kept the controlled group to teach

regular classroom curriculum assigned for that part of the school day, which was reading

and writing. She also gave me descriptions about students’ behavior and school

performance.

2. Age of the participants: 7 and 8 years old

3. Number of participants: 10 students

4. Participant recruitment plan: Thirteen out of nineteen of her students scored less than

70% in their benchmark test -topics 1 through 4- (see appendix 1). However, only ten out

of thirteen were part of the experimental group. Three students who scored under 70%

due to distraction when filling the bubbles in the test were left out of the intervention.

The setting for the intervention was a second-grade classroom of ELL students under the

English Transition Model (ETM), which is designed to help limited English proficient

students master the state curriculum while learning English

5. Timeline of activities (including date and time): second and third weeks of November

2014. The time of the activities changed accordingly to collaborative teacher schedule,

and time assigned for the activities were reduced greatly.

November 12. Pre-test

-One-digit addition and subtraction word problems (appendix 2)

-One-digit addition and subtraction worksheet (appendix 3)

November 13. Pre-test

-Two-digit addition and subtraction pre-test (appendix 4).

November 14. Addition and subtraction up to ten using concrete models.

-Students will count objects such as bears, base ten blocks or tiles

-Objects will be broken into two equal groups.

-Students will use number cards to build and break apart numbers

-Use symbols with the numbers to solve problems using algorithms

-Use fact families and missing addends

-This activities will help ELLs to build and conceptual understanding

November 18. Activities using ones, tens and hundreds charts, and one hundred chart

- Discussion of teen numbers using manipulatives and base ten blocks (11 is 1 ten

and 1 one, 12 is 1 ten and 2 ones, etc.)


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- Do the same with 20s

- With 10 blocks illustrate adding with 10. Break apart to make a 10

- Explore how the ….ty numbers are made up of some tens.

- Write numbers in different ways (45, forty five, 40 + 5)

- Look at how numbers are related to each other on the 100’s chart by mapping out

patterns of 10’s and 1’s

November 20. Adding and subtracting 2 digit numbers

- Addition and subtraction using multiples of 10 using base ten rods

- Use of place value cards

- Solve problems like 20+30= ___, 50-30=____, 50+____=70

- Addition and subtraction using 2 digit numbers with regrouping

46+37=(40+6)+(30+7)

November 21. Post-test. Two-digit addition and subtraction worksheet (appendix 5).

6. Materials and resources required: Construction paper, personal white boards, dry

erase, dice, card numbers, bears, dinosaurs, tile pieces, chips, one hundred tables, place

value tables, dice and base-ten blocks (one centimeter cubes represented the ones, a tens

rod represented ten cubes, and a hundreds flat represented hundred cubes) which were

the main hands-on item. This blocks allowed students to see the expanded form o a given

number.

7. Plan to obtain these materials and resources: Collaborative teachers provided me with

the material needed for the activities. Another teachers and the researcher provided more

of the materials required to use during the interactive activities.

8. Safety consideration: It was a regular setting with safety regulations. The teaching

method did not compromise students’ safety. The researcher followed school rules by

signing in and out whenever she went to perform the activities. She was also careful not

to take pictures of the faces of the children because she did not obtain necessary permits.

9. Scientific topics involved: 9. Basic addition is the process of uniting two or more

numbers into one sum represented by the symbol +; subtraction is the action of finding


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the difference between two numbers; place value is the position of a digit in a number;

hundred chart is a tool that shows numbers from 1-100 in order; manipulative is a tool

used in math to assist in figuring out the answer; number line is a tool that shows

numbers in order and goes on forever in both directions; regrouping is when 10 ones can

be put together to make a 10 or when a 10 can be broken down into ones, also known as

carrying and borrowing; number sentence is numbers from the problem shown with the

correct operation in order to solve the problem, also known as the equation.

1. Formative assessments: Students were tested with word problems in English language

to evaluate language proficiency. During the testing all of them asked constantly for

translation of sentences into Spanish and they scored very low. Afterwards, they were

tested with a worksheet where no real-life context was included (just two-digit addition

and subtraction). Most of them did not perform well. The journal for observation of

student engagement and performance during the math activities recorded my perceptions

and observations during the implementation of the activities and testing. It shows

students' engagement in activities but they found testing boring. I also observed eye

contact between myself and students. Reflecting on the intervention, I found out that

reading a trade book at the beginning of the lesson should be included to relate addition

and subtraction to everyday situations. Thus, students will be more engaged during the

presentation of real-life context activities. The journal quantitative data indicates students'

engagement during math activities. Students observation and records in a journal. One

digit addition and subtraction for the classroom, there are a lot of formative assessments

in which we can imply in the classroom to monitor our students’ learning and see if they

are actually grasping the concept that is being taught by my cooperating teacher and

through the observance of their participation seeing their attitude towards what they are

learning. One form of formative assessment that was used to see the students showcasing

their understanding of its completion. A comparison on how students answer the pre and

post-test showed if the use of manipulatives, hands-on activities, and group work

improved student understanding of addition and subtraction using base-ten model. This

data collection allowed me to collect quantitative data in a short period of time (Mills,

2011).

Another data collection tool used in evaluating students’ performance while doing

hands-on activities, was the record of observations in a journal. The observations focused

on student engagement during hands-on activities and attitude during the instructional

process. Observations were used to help me determine students' engagement and

understanding of the concepts.

2. Summative assessments: The post-assessment consisted on two-digit addition and

subtraction (see appendix 5). A word problem test was originally planned to assess students. However, the lack of time prevented to do it.

D. Project Evaluation Result


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1. Evaluation Result The research findings mention the importance of helping students

understand the underlying mathematical idea about addition and subtraction. One of the

problems with students is lack of vocabulary in both English and Spanish. They like to

read but they pay more attention to the pictures. Their parents do not communicate with

them using an extent vocabulary because they lack vocabulary as well. Although they get

the idea of adding and subtracting, when reading math problems they do not know what

to do.

The table shows the data corresponding to pre and post-test. It also shows the overall

average of both tests and an improvement average of 10 points. Six of the nineteen

students did not progress to a satisfactory level in the activities. It is worth mentioning

that student number one made a little mistake due to distraction (he was bored during the

testing). Most of the students improved their scores after the intervention. Gathered data

shows that the implementation of the activities was somewhat successful, and the

students improved their performance in adding and subtracting two-digit numbers.

The journal for observation of student engagement and performance during the math

activities recorded my perceptions and observations during the implementation of the

activities and testing. It shows students' engagement in activities but found testing boring.

I also observed eye contact between myself and students. Reflecting on the intervention, I

found out that reading a trade book at the beginning of the lesson should be included to

relate addition and subtraction to everyday situations. Thus, students will be more

engaged during the presentation of real-life context activities. The journal quantitative

data indicates students' engagement during math activities.

The study found student improvement regardless of lesson delivery, and improved

engagement with introduction of everyday math. As a result of this study, introduction of

more everyday math in the second grade classroom can lead to better engagement

responded positively to activities and researcher was able observe a slight improvement.

Only one child struggled understanding numerical concepts and the activities. More work

needed with him. I noticed that some the students did not pay attention in the beginning

of the project and did not follow directions properly.

1 100 95 05

2 50 80 30

3 0 55 55

4 80 70 10

5 60 65 5

6 55 60 5


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7 55 80 25

8 60 70 10

9 70 70 0

10 40 55 15

11 60 55 5

12 65 65 0

13 0 0 25

14 45 50 5

15 5 30 25

16 55 65 10

17 60 75 15

18 50 60 10

19 50 60 10

Average 51 61 10

When observing the classroom, it seemed as if the students truly enjoyed the interactive

activities. Math time was before lunch. Mrs. Schoenbrun tended to start math instruction

before lunch and used guided reading time to settle students down a little in order to

move on with the rest of the day’s activities and lessons.

2. Project activity pictures (at least 10 pictures that capture the essences of the project,

these pictures will be posted on Dr. Hsu’s website).


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E. Discussion (how do the results relate to other research findings?

The results of this study intervention and other research studies about second grade

performance exceeded the results obtained during usual instruction. Findings in this study

and others showed that students perform better when a non-traditional instruction is

implemented. Other research studies showed that more time were needed with some

children. Likewise, this action research required more time to reflect better results. In

addition, manipulatives were a great support for students’ thinking but it took time to

transfer the “concrete” into written addition and subtraction. Reflecting on the

intervention, I found out that reading a trade book at the beginning of the lesson should

be included to relate addition and subtraction to everyday situations. (Wilburn, Keat &

Napoli, 2011). “A remainder of one” by Elinor Pinczes and Bonnie Mackain (2002)

could be a good choice. This book introduces a regiment of 25 beetles on parade. Their

blue bug queen "likes things tidy," and when the bugs march two by two, she notices that

one bug brings up the rear. Therefore, students will be more engaged during the

presentation of real-life context. As a result of this study, introduction of more everyday

math in the second grade classroom can lead to better engagement.

The goal was to help students understand addition and subtraction using base-ten

blocks. The researcher had to make changes in schedules and time duration of the lessons

leading to an undesired outcome. The researcher is planning on doing more research


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about effective teaching methods that use manipulatives, hands-on activities,

paired/group work (centers) and technology.

Manipulatives and hands-on activities as mathematical instructional tool helped

students and the researcher to improve because of engagement during the activities.

Action research entitles a lot of effort, but it is a wonderful tool to improve teaching

methods. As educators, it is recommended to look for professional development and

action research provides awareness of the possibilities in helping students succeed in their

education.

F. References

Bresser, R., Felux, C. & Melanese, K. (2009). Supporting ELLs in Math class. Math

solutions. Retrieved from: http://mathsolutions.com/wp-

content/uploads/09_CMSI_ELL.pdf

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S.B. (2015).

Children's mathematics: Cognitively guided instruction. Portsmouth, NH:

Heinemann.

Champagne, Zachary, Schoen, Riddell & Claire (2014).Variations in Both Addends-

Unknown Problems. Teaching Children Mathematics. Sept. 2014, Vol. 2. Issue 2,

pp. 114-121.

Jarret, D. (1999). The inclusive classroom. Teaching Mathematics and Science to

English-Language Learners. Mathematics and Science Education Center.

Retrieved from: http://educationnorthwest.org/sites/default/files/11.99.pdf

Lai & Murray (2012).Teaching with Procedural Variation: A Chinese Way of Promoting

Deep Understanding of Mathematics.

Lai, E. R. (2011). Critical thinking: A literature review. Pearson.

Mills, G. (2011). Action research: A guide for the teacher researcher (4th ed.). Boston,

MA: Pearson.

Parrish, S., (2014). Number talks. Helping children build mental math and computation

strategies. Math solutions. Sausalito, California, USA.

Shaw, J. M. (2002). Manipulatives enhance the learning of mathematics. University of

Mississippi. Retrieved from: http://eduplace.com/state/author/shaw.pdf.

Thanheiser, E. (2012). Understanding multi-digit whole numbers: The role of knowledge

components, connections, and context in understanding regrouping 3+- digit

numbers. Journal of mathematical behavior 31, 220-234


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Tzur, R., Johnson, H. L., McClintock, E., Kenney, R. H., Xin, Y. P., Si, L., Woodward,

J., Hord, C. & Jin, X. (2013). Distinguishing schemes and tasks in children’s

development of multiplicative reasoning. PNA, 7(3), 85-101.

Tzur, R. & Lambert, M. A. (2011). Intermediate Participatory Stages as Zone of Proximal

Development Correlate in Constructing Counting-On: A Plausible Conceptual

Source for Children’s Transitory “Regress” to Counting-All. Journal for Research

in Mathematics Education. 2011, Vol. 42, No. 5, 418–450

Verzosa & Mulligan (2012). Learning to solve addition and subtraction word problems in

English as an imported language.

Wilburn, J., Keat, J., & Napoli, M. (2011). Cowboys count, monkey’s measure, and

princesses’ problem solve: Building early math skills through storybooks.

Baltimore, MD: Brookes Publishing Company.

G. Appendixes


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A. Project Rationale Teaching second grade ELL...

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