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1Running head: IMPROVING ACHIEVEMENT THROUGH WRITING

Improving Student Achievement in Math, through Writing

Celeste Over

EDU 699

Dr. Therese Ajtum-Roberts

IMPROVING ACHIEVEMENT THROUGH WRITING 2

Abstract:

This capstone project infuses a series of writing lessons into the already challenging

Algebra and Pre- Algebra curriculum that is aligned to the Common Core State Standards. A

baseline assessment was administered followed by six instructional lessons covering the main

idea and appropriate organization, while emphasizing mathematical content. While these writing

lessons do not specifically utilize the models of curriculum such as understanding by design, the

lessons were embedded into the Windsor 6-8 math curriculum which was written utilizing that

design model. As a result, these lessons utilized assignments already in the curriculum while

adding a writing component. Therefore, the math content has been enhanced and not

compromised. The goal of the capstone project is to improve student achievement and reduce

the achievement gap between white and minority students. The eight grade teachers infused the

writing strategies in their lessons, and students were given the opportunity to practice these

strategies. The teachers who implemented the writing strategies provided feedback and reflected

on their experience and effectiveness of implementing these lessons into the Math curriculum.

Rationale

NCTM encourages school districts to infuse writing in their mathematic curriculums in an

effort to allow students to communicate their mathematical thinking and ideas. If students

struggle with math concepts, writing to improve their critical thinking skills, writing beyond

writing to learn but to demonstrate learning, can help students develop their ability to analyze

and problem solve; thus improving achievement (Kostos & Shin, 2010).


The Connecticut Common Core standards in math, encourages students to approach

complex math problems by explaining the meaning of the problem, make conjectures, and

construct viable arguments (CCSS, 2012). Writing promotes critical thinking, reasoning,

communication skills, thus mathematically proficiency will increases when students write

(Kostos & Shin, 2010).

In almost every academic area African American and Hispanic students perform at lower

levels in comparison to their white counterparts. According to the National Assessment of

Educational Progress (NEAP) 45 percent of White students versus 14 percent of African

American and 21 percent of Hispanic students in eight grade score at or about proficient in math

(Achievement, Gap, 2014). In the area of writing, 46 percent of white students versus 17 percent

of African American and 22 percent of Hispanic students in the eighth grade scored at or above

proficient. (Achievement, Gap, 2014). The placement of African American and Hispanic

students in special education and their underrepresentation in the gifted and talented programs

provides inequities which manifest itself through underachievement in math (Douglas, 2008).

This placement of minority students in special education classes significantly impacts their

educational success and impedes the student’s ability to achieve at the same rate of their white

counterparts. As a result, minority students are plagued with low expectations, ineffective

teachings and in many cases fulfill a preconceived notion that the minority student cannot

achieve (Douglas, 2008). Encouraging all students to write regardless of race, and cultural

backgrounds will improve achievement. Allowing students to connect to relevant situations in

their lives through writing will also improve achievement (Bennett, 2011).


Research

The achievement gap refers to “systematic variances in the ability to learn between

students from majority populations and students from minority populations” (Achievement Gap,

2014,

p. 1).

Minority and low-income students are less likely to have access to enroll in and succeed

in higher-level math courses in high school than their more advantaged peers. Therefore

achievement for minority students in math is a function of being locked out of challenging

rigorous courses and not a function of intellect (Wang, 2009). There are clearly inequities by

race. Studies confirm that about 17% of Black and Hispanic graduates take higher level math

such as trigonometry and Algebra II compared to about 83% of their white peers (National

Center for Education, 2012). Nationally about 17% of the U.S 12th graders are prepared for and

interested pursuing careers in mathematics. Minority students may indicate interest; however

lack the necessary proficiency in math to successfully engage in education to achieve success in

these careers. Again, the problem is seen as lack of opportunity, not ambition ( Adelman, 2006).

Research provides options for minimizing the gaps which includes cultural education for

teachers, early intervention, and mentoring (Scott, 2013). In addition writing in math beyond the

explaining of process improves achievement (Craig, 2011). Language and vocabulary are

essential for human interaction and human thought. Using language to encourage students to

develop concepts, develop new ideas, and organize their understanding of relationship to make

predictions to help understand the world around them will enhance their understanding of


mathematics (Adams, 2010). Research shows that writing to learn differs from writing to

demonstrate learning. When students write to demonstrate learning, mathematical process such

as interpreting, reflecting, justifying one’s thinking, predicting, and observation of patterns, can

play a vital role in developing mathematical literacy and understanding (Meyer, 2014). When

students write to learn, the writing is focused on recording and factual content accuracy. Since

the content may be memorized this form of writing serves as a record as what was learned and

may be assessed for errors (Meyer 2014).

Contribution to Education

This capstone project provided another strategy for educators to implement to combat the

achievement gap. The approach to shrink the achievement gap has primarily been to align the

curriculum with the student’s culture and ensure the curriculum is relevant to student’s lives

(Scott, 2013). The approach has been centered on addressing lack of skilled cultural teachers,

eradicating low educational expectation, involving families, and providing mentors for students

of color (Scott, 2013). While the strategies listed above are important factors, one cannot ignore

the role writing can play in increasing achievement across all content areas. Educators can

develop tasks that involve student’s choice, provide authentic writing opportunities, and

demonstrate models for students to produce writings that create student discourse, and encourage

them to make decisions that go beyond the obvious. Providing the opportunity to participate in

rigorous math classes must be accompanied by the tools to make this participation successful.

Writing to demonstrate learning can be that tool. Early exposure to writing in math to increase

achievement must begin with kindergarten aged children and must include a range of appropriate


experiences, including but not limited to, making relevant connection to the student’s lives

(Wang, 2009).

Contribution to Personal Skills

Upon completion of this project the researcher obtained the skills to integrate writing into

a math curriculum in a meaningful, purposeful and effective ways. The emphasis was placed on

writing to demonstrate learning in addition to writing to learn. Teachers of math are skilled in

encouraging students to write to explain procedure and process. However, the CCSS places

additional emphasis on decision making, critical thinking, and producing writing that encourages

student discourse in student centered classrooms. In an effort to increase the achievement in

math, teachers developed skills where choice of writing was provided for students that do not

compromise delivering curriculum content.

Project Details

The goal of this capstone project is to increase achievement of all students in math by

providing students with opportunities to demonstrate their understanding of mathematical

concepts in writing. Since there is a significant achievement gap between the achievement of

white students and African American and Hispanic students, the ultimate goal is to reduce the

achievement gap by infusing writing into the math curriculum already aligned with the Common

Core (Achievement Gap, 2014).

The 8th grade math teachers in the middle school have instructed 6 lessons with emphasis

on conveying the main idea clearly, putting properly labeled calculations and facts into words


clearly, providing detailed support and elaboration, logical sequencing, providing a strong

beginning and conclusion, and using effective transitions.

Pre-Algebra Lessons:


Algebra Lessons:


All students have completed a baseline assessment called mathography. (See Appendix A)

Additionally opportunities were provided for students to put these strategies into practice. One

writing opportunity was administered in two Algebra classes (See Appendix B) when patterns

were covered and another opportunity to practice the strategies administered in the Pre-Algebra

classes, when real numbers and square roots were taught (See Appendix C). The base line

assessment and the instructional lessons utilized activities already present in the curriculum. The

instruction included modeling of each facet of writing and the writing was evaluated using two

rubrics, one scoring the main idea and application, and the other the organization and sequencing

of the writing. The instructors demonstrated/modeled for the students specifically how to

accomplish writing through thinking and also demonstrated how to express out loud the

decisions they made as a writer. Strategies have been reviewed with students and methods to

accomplish the writing objectives were clearly defined. Daily opportunities were provided for

students to practice writing about and to extend learning. These daily opportunities, such as

warm up, were not scored using the rubric; but provided informal opportunities for students to

express understanding through writing. In providing these opportunities, the students recognized

the importance of writing every day in math.

In more involved assignments, the teachers facilitated opportunities for student discourse

around writing and provided actionable feedback. After the instructors taught the lessons and

opportunities for students to practice writing was evaluated, teachers provided feedback about

the writing lessons and reflected on their experience and effectiveness of implementing the

writing lessons into the Math curriculum. (See Appendix D) Because most of the feedback was

positive, teachers of other content areas will be exposed to the rubrics and encouraged to adjust

and tweak the rubrics to fit their specific content area.


Project Outcomes

This project provided writing lessons that were implemented into an already established

Algebra and Pre-Algebra curriculum. Teachers instructed students on writing to demonstrate

understanding of the main idea of the mathematical problem, and extend learning. The goal of

the capstone project is to improve student achievement and reduce the achievement gap between

white and minority students. This capstone project has also contributed to the middle school

improvement plan. Currently the middle school does not have a school wide writing program.

Direct instruction of writing only takes place in Language arts classes and there is no minimal

established expectation for writing. An analysis of writing performance data over three years at

the middle school indicated that writing compared to other tested area is an area of weakness and

has shown the least amount of growth. As a result, teachers in all content areas are expected to

infuse writing in the already established district curriculum (Windsor BOE, 2012).

M.Ed. Outcomes

This project has demonstrated the following program outcomes:

1. Students will be able to identify, analyze, evaluate and implement research-based

educational practices matched to an area of concentration.

2. Students will develop expertise in designing and delivering instruction to support the

achievement of a diverse population of learners of all ages in a variety of settings.

These outcomes were realized as teachers implemented writing strategies within the 8th grade

math curriculum. Wang (2009) states that early exposure to writing in math will improve

student achievement. Upon examination of student’s scores on standardized testing, and


analysis of practice, it was concluded that writing needed to be a part of our math curriculum.

Teachers were surveyed from all content areas and 77% of our teacher believed in order for

our students to perform well in all content areas, they needed to write well. In the middle

school, writing was only taught in Language arts classes yet there was an expectation that

students would understand how to write in math, science, and other content areas that did not

specifically teach writing. As a result, teachers from all content areas were urged to create

writing lessons specific to each content area. In each content area, baseline data was collected

to identify specific weaknesses, and an analysis of practice was done. Once the problem was

identified, practiced analyzed, lessons were developed to infuse writing into the math

curriculum.

The student population of Windsor is very diverse; therefore sensitivity to the culture

and relevancy to student’s lives was evident in this project as students write to demonstrate

learning. One example of a writing activity that is sensitive to the student’s culture is the

IPod writing task. In the writing activity, the students were asked to write a Hot Technology

column for the school newspaper The Hoofbeat. The assignment gave the scenario where the

Algebra 1 teachers each received a $500 Apple Gift card from a successful (and grateful)

WHS graduate, and they’d like you to do a comparison of the iPod models currently available

and make a recommendation for each of them. In teams students selected to help the

following teachers.

• Ms. DeBay wants to buy new songs to listen to while hiking. She also wants to upload 10 of

her Beyoncé CD’s and 2 of her Taylor Swift CD’s.


• Ms. Over wants to buy HD movies, especially comedies. She already has 10 of them to

upload.

• Ms. Orzechowski wants to buy old songs and wants to upload 2500 pictures of her family.

• Mr. Chiang wants to buy R & B albums and wants internet access for Pandora.com. He also

wants to upload his collection of 100 CD’s.

• Ms. Lazlo wants to buy TV Shows. She also wants to upload all three of the Twilight

movies she already has on her computer. By allowing students to select the teacher of their

choice, the assignment recognized the diversity of the student population. Appendix J

demonstrates the student’s ability to write and explain understanding of the task.

Concentration in Teaching and Learning outcomes realized will be

1. Students will be able to use selected advanced instructional strategies appropriate for

specific learning outcomes.

2. Students will be able to apply a variety of formative and summative assessment strategies

to evaluate and improve teaching and learning.

Writing to increase math achievement was a new instructional strategy used with this

population of student. All students both Algebra and Pre-Algebra were given a base line

assessment called Mathography (see appendix A). Samples of students work confirmed that

the students in the eighth grade did not understand how writing in math could improve

achievement. The work completed solidified what the students had verbalized to their

teachers; they did not see the value in writing in math. The work of two students is included


to indicate how the writing lessons improved their ability to explain their mathematical

reasoning and demonstrate learning. Through discussions with the teachers who implemented

the writing lessons, the students embraced expressing the main idea, including calculations

with labels, and providing details that indicated understanding of concepts; however, they did

not embrace the organizational portion of the mini lessons. The students resisted included

transition words in their writing. The teachers also indicated that they themselves did not

embrace the organization traits of the mini lessons; seeing this trait as unnecessary to

demonstrating learning in math. In reviewing student work, it also appears that the teachers

did not emphasize demonstrate learning beyond the obvious but instead encourage students to

support their conclusions with mathematical facts and calculations.

In reviewing the work of the Pre-Algebra student, growth in writing and explanation of

mathematical concepts is clearly evident. In the mathography the student explained that he

enjoyed fractions, but his explanation as to why is somewhat elementary. There are no

specific examples to support the student’s love of fractions. (See Appendix E) In the moving

box problem some growth in the student’s writing. He explained the task, and attempts to

explain his calculations; however there are several errors in his explanation and labels. (see

appendix F). In the assignment, Mr. Cavaliere’s front walk, it is evident that this student has

demonstrated improvement. The student answers the question, explains the calculations, and

provides a conclusion based on the calculations (see appendix G and H). The inclusion of

these examples from the same student demonstrates growth in writing and the understanding

of math from the mathography assignment to Mr. Cavaliere’s Front Walk.


In reviewing progress of the Algebra students, growth is also evident in the work and the

ability to express understanding of mathematical concepts through writing. These students

are high achieving and the mathography included indicates that this student can explain in

words why problem solving is a preferred concept in math and shared example of when

problem solving was utilized (see appendix I). In examining the same student’s work with the

IPOD performance task, this student shows significant growth in using writing to explain her

thinking. In her answer, the student demonstrates understanding of the task, fully explains the

calculations, and makes a recommendation which is supported by those calculations (see

appendix J). In both Algebra and Pre-Algebra classes, after students were instructed using

the mini writing lessons, their work indicates an improved ability to communicate their

thoughts and reasoning through writing.

Technology

On an ongoing basis student utilize the TI-86 graphing calculator along with chrome

books. The students completed some of their assignments utilizing the chrome books and

Google classroom. One of the requirements of the mini writing lessons is to demonstrate

learning by elaborating and providing supporting details that goes beyond the obvious. In

completing this elaborating piece, the students were asked to demonstrate understanding by

providing another scenario utilizing mathematical skills similar to the ones being practiced.

The internet was used as a resource to assist students in this aspect of the writing. However,

in the area of elaboration the students continued to struggle. Technology was also utilized as

the lessons were delivered by the instructors through the use of PowerPoint slides. These

slides will be accessible to the students and shared with the school community through


Google Drive and a website. Teachers were asked provide ongoing feedback through the

comment section of the website.

Project Evaluation

Evaluating the effectiveness of the writing strategy and the writing lessons will rest

specifically on the perception of the teachers who implement the writing strategies in their

classrooms. Instructors have been asked to evaluate the ease of using the rubric as an

assessment tool, the ease in which the lessons fit into the existing curriculum and the whether

the task were relevant to the students lives. The instructors have also been asked to give their

opinions on the effectiveness of the use of the writing strategies to increase achievement in

math. Finally the teachers have been asked to give their opinions on the ease of using a

similar strategy for other content areas. In other words, will the middle school be able to use

this rubric as a school wide assessment tool.

In reviewing the feedback and reflection from the teachers who implemented the

writing lessons, the teachers felt the writing had a positive effect on achievement. Both the

Algebra and Pre- Algebra teachers specifically commented on the fact that students were

asked to extend beyond the obvious by applying learning to real life, providing a picture of

how math topics can be used. Teachers also praised the rubrics and model lessons for

specifically detailing the expectations. Another important point emphasized was the fact that

the writing tasks were authentic in that they related to the student’s lives. The students were

asked to assist their principal in the Front Walk problem (Appendix G and H). The fact that

the school principal was “real” person to the students significantly increased the authenticity

of the task. One Algebra teacher did not feel the example used in the mini lesson around the


tennis club was relatable to our students, although did acknowledge that the situation is a

plausible one.

One teacher specifically mentioned the use of the RACE acronym in teaching

organization. However, in all cases, the teachers stated the students struggled with the

organization aspect of the mini lessons. One teacher felt strongly that the organization lessons

did not apply to the math classroom. The organization portion of the writing lessons will need

to be re-examined. While good organization enhances writing, the teaching of this skill may

in fact belong in the Language Arts classroom and not the math classroom. If students write

an adequate main idea, support the calculations with an appropriate explanation that goes

beyond the obvious, then the organization piece specifically using transitions words may not

in any way add to math achievement. Therefore, the organization lessons are a weakness of

this project.

Overall, teachers were receptive to having students demonstrate knowledge of math

concepts through writing. They felt it enhanced and improve learning and achievement.

They found the lessons relatable and easy to implement into the math curriculum. See

teacher’s responses in Appendix K.

Reflection and Discussion

The teachers who implemented the writing lessons viewed these lessons positively; and

concluded that the students being asked to demonstrate knowledge by extending their leaning

and applying knowledge to real life was beneficial. It was also suggested by these teachers


that the organization lessons be eliminated from the math writing lessons, and left to other

content areas such as History and Language Arts. The math department will adapt the ideas

trait portion of the writing program; however the organization trait will not be a part of the

writing program.

The adaption of the writing program is a huge step for the middle school which identified

writing as a major deficiency for the students. In a school wide PD, the entire program was

introduced to teachers of all content areas. At that time, each content area teacher had the

opportunity to adapt the similar lessons and adjust them so the lessons work for their

students.

In completing this project I have gained strategies to improve teaching and learning. This

capstone project has pushed me to think about different strategies to improve my student’s

achievement. Math is more than just numbers, therefore encouraging student to apply

knowledge through writing, explain thinking through writing, and elaborate beyond the basic

calculations has improved my student’s ability to understand and learn math.

A capstone project that uses writing as a strategy to teach math was not my first choice;

however as the project unfolded, I embraced the research and work that suggested that

writing could enhance the learning of math. Math is my passion, writing is not. However,

throughout the master’s program, I have been asked to step out of my comfort zone and this

capstone project was another way in which I grew professionally because stepping out of my

comfort zone became more comfortable. In selecting a teaching and learning concentration, I

sought a project that would improve my teaching and improve my student’s and my own

learning. All education professionals should seek new strategies to improve their practice,


even if these strategies are somewhat uncomfortable and seemingly out of their comfort zone.

As professionals we must continue to learn, reminding ourselves that like our students, we

are professional learners.


References

Achievement Gap. (2014). Research starters, academic topic overviews. EBSCO Information Services

Adams, A. (2010). Rehearsal or reorganization two patterns of literacy strategy use in secondary

mathematics classes. The Montana Mathematics Enthusiast 7(2), 371-390.

Adelman, C. (2006). The toolbox revisited: paths to degree completion from high school through

college. Washington, D.C: U.S. Department of Education.

Bennett, C.I. (2011). Comprehensive multicultural education: Theory and practice. (Seventh Edition)

Boston: Pearson.

Common Core State Standards Intiative. (2012) Retrieved from http://www.corestandards.org

Craig, T. S. (2011). Categorization and analysis of explanatory writing in mathematics. International

Journal of Mathematics Education in Science and Technology, 42(7), 867-878.

Douglas, B., Lewis, C.W., Douglas, A., Scott, M., Garrison-Wade, D. (2008). The impact of

white teachers on the academic achievement of black students: An exploratory qualitative

analysis. Educational Foundations, 47-62.

Kostos, K., Shin, E. (2010). Using math journals to enhance second graders communication of

mathematical thinking. Early Childhood Education Journal 38 (4), 223-231.

http://www.corestandards.org/


Meyer, K. (2014). Making meaning in mathematics problem-solving using the reciprocal teaching

approach. Literacy learning: the Middle Years, 22(2), 7-14.

National Center for Education Statistics. (2012). High school coursetaking: Findings from the

condition of education 2012. Washington DC: U.S. Department of Education. Indicator 31-2012.

Scott, J., Taylor, K., Palmer, R. (2013). Challenges to success in higher education: An examination

of educational challenges from the voices of college-bound black males. The Journal of

Negro Education, 82(3), 288-299.

Wang, A. (2009). Optimizing early mathematics experiences for children from low-income families:

A study on opportunity to learn mathematics. Early Childhood Education Journal, 37(10), 295-302.

doi:10.1007/s10643-009-0353-9


Appendix A

Name _____________________________ Date _______ Period___

“Mathography” Writing Assessment

It is important to get to know you as a math student and as a writer.

Directions: Choose one of the following topics to write about. Be sure to answer the question clearly using a detailed explanation, accurate mathematical examples, and strong organization.

Choice 1: What is one mathematical activity/lesson that you enjoyed? Explain what the activity/lesson was using specific examples and why you enjoyed it.

Choice 2: What is one mathematical activity/lesson that can be used in a real life situation? Explain what the activity/lesson is using specific examples and how it can be helpful.

Use this space provided to plan your calculations and writing.

Appendix B (Algebra)


Name: _______________________ Date: _______________ Period: _____Algebra I

Writing Practice Unknown Weights

Directions: Read the problem carefully and provide a thoughtful written response. Be sure to answer the question clearly using a detailed explanation, accurate mathematical examples and strong organization.

Identify the weight of each object from the relationships shown on the scales below. Show all work and write a detailed description of the steps you used to solve the problem.

Cylinder = ______ units Cube = ______ units

Sphere = ______ units Tall rectangular prism = ______ units

Appendix C (Pre-Algebra)

Name: _________________________ Date: _________ Per: ________


Writing Practice

Moving Box Problem

Directions: Read the problem carefully and provide a thoughtful written response. Be sure to answer the question clearly using a detailed explanation and accurate mathematical examples.

Jason’s family is moving out of their house. His mom gives him a cardboard box in the shape of a cube with a surface area of 1350 cm2 to pack up some of his belongings. Jason has another cubed shaped box already packed with his personal belongings that has a volume of 4096 cm3. Could Jason’s box fit in the box his mom gave him?

Appendix D- Teacher feedback

Writing in Math Mini Lesson Reflection

Thank you for agreeing to instruct the mini writing lesson in your math classes. Please take a moment to reflect on the experience by answering the following question.


1. Before the writing task, what are some strategies you used in your classroom to prepare your instruction?

2. During the writing task, what are some strategies you used to help students complete the task to the best of their ability?

3. How were the writing tasks authentic?

4. How did implementing these writing strategies affect student achievement in math?

5. Additional comments about the experience.

Appendix E- Mathography Student Work Pre: Algebra


Appendix F- Moving Box Student Work Pre: Algebra


Appendix G- Mr. Cavaliere’s Walk

Mr. Cavaliere’s Front Walk

Mr. Cavaliere is having a new front walkway installed at his house on Ash Road. He wants the walkway to be a rectangular path with an isosceles trapezoid at the end where the walkway meets Ash Road. The contractor provided a quote of $2000.00. The contractor stated they charge a flat fee of $200 and charge $12 per square foot of concrete needed for the walkway. The bill also includes 6.35% sales tax. Mr. Cavaliere feels that the quote is too high and has asked you to use the skills you have learned in Pre-Algebra to help him to determine if the price quoted is reasonable.

On a separate piece of paper, provide an explanation to Mr. Cavaliere. Include calculations to support your conclusions. You may do work on the diagram above and reference your work within your explanation. Your final explanation must be clear, reference/show your calculations, provide a recommendation for Mr. Cavaliere.

Appendix H- Mr. Cavaliere’s Walk Student Work Pre: Algebra


Appendix I- Mathography Student Work Algebra


Appendix J- IPod Student Work Algebra


Appendix K- Teacher Reflections

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