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Producing More Problem Solving by Emphasizing Vocabulary Producing More Problem Solving by Emphasizing Vocabulary
Jill Edgren
Grand Island, NE
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Producing More Problem Solving by Emphasizing Vocabulary
Jill Edgren
Grand Island, NE
Math in the Middle Institute Partnership
Action Research Project Report
Impartial fulfillment of the MAT Degree
Department of Mathematics
University of Nebraska-Lincoln
July 2008
Producing More Problem Solving by Emphasizing Vocabulary
ABSTRACT
In this action research study of my Algebra 1 and Algebra 2 classrooms with ninth to eleventh
grade students, I investigated word problem completion while emphasizing vocabulary. A word
wall was implemented along with notes organizers, vocabulary sheets, and written definition
during class. Data was gathered about attempts and completion of mathematic word problems on
daily assignments, quizzes, journals and tests. Through observation of student work, surveys,
interviews, and in class word problem journals, I discovered that many students are least likely to
do word problems on assignments, then tests, and most likely to complete word problems on a
quiz. As a result of this research, I plan to clarify expectations and emphasize vocabulary more
purposefully for each student, as many students were indifferent to the word wall.
More Problem Solving 1
I. INTRODUCTION
The purpose of my action research was to determine if emphasizing vocabulary would
result in an increase in word problem completion. I become highly frustrated when word
problems are often neglected and not completed on assignments and assessments. I have a few
ideas as to why students would do this that are addressed through the rubrics on the homework.
In my ideal classroom, students would be motivated to learn with a peaked curiosity of
how all math concepts fit together. Since becoming a part of Math in the Middle, I learned that
more meaningful and situational problem solving benefits students and often allow them to learn
more deeply and cohesively. For this reason, I assign more word problems through the text I use
than I previously have. Multiple students come in before school not even comprehending or
understanding the word problems. Other students in the halls realize nobody in their group of
friends understands it either, thus they choose to leave it completely blank. I know these
problems and the solving processes involved are very important and I want all students to
competently complete these problems. However, I find myself doing the problem while a few
pay attention and learn one problem at a time.
This study is important to me for several different reasons. This could show me how
beneficial emphasizing vocabulary is for my students. Could it increase student ability to
understand word problems and then complete them? Many of my students would much rather
just skip the words and complete an explained algorithm of steps to solve an explicit question.
My administrator was expecting a word wall in every room. This research project could show
that the time spent creating and implementing a word wall was is well worth it. My concern is
that students will still not learn meaningful mathematics and will be oblivious to the mathematics
surrounding them through this process.
More Problem Solving 2
II. PROBLEM STATEMENT
For education in general, this action research project hoped to show that making changes
to incorporate more meaningful and rich in contextual mathematics would influence student
performance. Teachers need to be certain students work with the knowledge they are gaining and
apply it, so the information becomes a part of the long-term memory. In order to apply the
information students must understand the mathematical terms used to describe and explain the
process. Hopefully students will realize that teachers are not merely concerned about a correct
response and sometimes the process is more important, even if a mistake is made. I believe
students need to be challenged and held accountable for their thinking.
The NCTM process standards specifically address the importance of problem solving.
Obviously this problem of practice deals with problem solving. Each student needs to be able to
apply his or her mathematical knowledge in another context. The other four process standards
are also involved in problem solving. Students must make connections between concepts and be
able to apply math in the real world possibly using representation as a part of the strategies and
reasoning to verify their solution, which must be communicated somehow. Problem solving
solutions communicated precisely show an understanding of the situation, problem and
mathematical ideas involved. These standards more likely come forward when a teacher probes
students asking how they came up with a certain answer or why they took a specified step or
approach.
III. LITERATURE REVIEW
Problem solving has become an area of emphasis for national mathematics standards. In
order to solve a word problem, students must be able to read and understand the situation, then
be able to make a plan. Poor reading comprehension and low vocabulary inhibit students’ ability
More Problem Solving 3
to begin attacking a problem. A review of some literature involving achievement related to
vocabulary and problem solving shows that this need for improvement is ongoing. Several
authors noted how students and teachers communicate mathematics with its effects on
mathematical comprehension. The issues causing trouble as supported by research include
reading comprehension, mathematic vocabulary, vocabulary strategies, communicating
mathematics, and problem solving.
Reading Comprehension
Schools all around the United States are constantly working to improve student learning
and achievement. One focus already in place is reading and writing across the curriculum.
Students will model what they hear and read in their writing. However, for students not reading
on grade level, their success will be difficult to document. Seven schools in Iowa had students in
grades 3, 4, 5, and 6 participate in a study associated with the University of Iowa. Paul of
Profiles Corporation, along with Nibbelink and Hoover (1986) used readability formulas to
assess word problems requiring the same computations below, on and above grade level. The
study showed that students were unable to discern what information was needed and how to use
the information. Overall, the students did not excel at any grade level or reading level. Even
when only the minimal basic information supplied, two years below grade level, students were
unable to identify the problem or solve the problem. Blessman and Muszczak (2001) researched
the effect vocabulary has on reading comprehension in solving word problems. Blessman and
Muszczak stated “students often search the problem for numbers rather than attempting to
comprehend what is truly being asked in the problem” (p. 28). Fifteen and twenty years later,
students are still unable to read a word problem and comprehend the message to solve the
More Problem Solving 4
problem. Sadly, students often believe they must rely on the order of the numbers alone to
determine how to solve a word problem.
Fletcher (2004) conducted an action research project in Mobile, Alabama, studying how
reading and vocabulary affect gifted Algebra 1 and Precalculus students. Fletcher’s students
would read the text and take comprehension and vocabulary quizzes. Many students struggled at
first with the change in routine, but were good, motivated students whose scores improved,
demonstrating a deeper understanding of the mathematical concepts. With all the language
involved in mathematics, students experience overlapping vocabulary in various contexts
throughout the day. Kotsopoulos (2007) made a list of sixty mathematical terms and counted
their usage during 300 minutes of classroom discussion. On average, an identified term was used
once every twelve seconds. When students were asked about these terms students had difficulty
explaining mathematical terms upon inquiry and occupied much of the interviewing time trying
to exhibit understanding.
Whether students are unable to read and comprehend a word problem is related to many
ideas. After attempting to read and solve a word problem unsuccessfully, several students
developed their own strategy of discarding all words, looking solely at the embedded numbers.
Fletcher (2003) attempted to amend that strategy by giving quizzes and emphasizing vocabulary.
Today’s classrooms are very rich in mathematical vocabulary, as noted by Kotsopoulos (2007),
and need to continue this development to avoid further confusion. Ultimately, I want to be sure
that my students can read and understand a word problem before going on to the next step.
Vocabulary
In 1997, Yeryshalmy studied 35 seventh grade beginning algebra students in Israel. He
was piloting a new curriculum called Visual Mathematics and using some computer software
More Problem Solving 5
called The Algebra Sketchbook. Yeryshalmy found that through discovery the students who were
able to proficiently describe the concepts and terms were able to show it through the use of The
Algebra Sketchbook. Many students were able to find the relationship between terms with
numbers, words, graphs, and symbols similar to the level that a traditional teacher would
demonstrate.
Schoenberger and Liming (2001) carried out a research project with sixth grade general
mathematics and ninth grade special education students at two different sites. They recommend
teachers challenge themselves and students with higher expectations in learning, vocabulary, and
explanations. Schoenberger and Liming taught a specific list of vocabulary. They stated,
“Students should be able to use and understand vocabulary in order to think about and discuss
mathematical situations” (p. 27). Students must possess proficient means of communication
before being immersed in the language of a word problem. Both sites demonstrated a positive
effect from the vocabulary implementation through different activities. Blessman (2001) studied
42 fifth grade students and 15 fourth and fifth grade teachers. According to some surveys, all
involved students commented that they would rather learn concepts and vocabulary more in
depth than a breadth of material. Also a few students would like to leave the word problems out
altogether as they know those problems are more challenging. The teachers wrote on their
surveys that the students had a poor mathematic vocabulary and the text does not reinforce the
vocabulary as much as the computations.
Vocabulary can be very challenging, especially within the context of mathematics. Many
words used in mathematics are also used in daily conversation with different meanings. The
resulting confusion of multi-use words halts student learning. “A student’s inability to
successfully minimize interference can potentially undermine his or her ability to learn”
More Problem Solving 6
(Kotsopoulos, 2007, p. 302). My research intended to show that further emphasizing and
teaching vocabulary will clear the interference and allow students to better communicate
mathematics through all medians. Yershalmy (1997) used technology to teach vocabulary.
Students learn best through discovery, even the terminology and teachers need to continue
challenging students whether they like the work or not (Blessman, 2001). Since teachers have
more experience and know more about what is best for student learning they make this decision
on delivery and engagement..
Vocabulary Strategies
Several strategies to emphasize vocabulary were suggested and shown in the research I
reviewed. Holden (1999), in an opinion article, elaborates on several vocabulary activities:
grouping, association, visual, physical and a word chain method. Grouping often occurs naturally
within the text with terms being related to a common concept or process. Association of
similarities and differences is one way of linking mathematical terminology to pre-existing
knowledge. Visual and physical strategies get students more involved and the level of
engagement is directly related to the amount of material learned. Students are to use a visual
picture or a physical motion to coincide with each vocabulary word. These pictures and motions
may be related to the meaning of the term, the spelling or some other connection. Making a word
chain is a great way to get multiple exposures with a larger word bank on the wall. The last letter
of one word must also be the starting letter of the next (Holden, 1999).
Roti, Trahey and Zerafa (2000) conducted an action research project while at Saint
Xavier University of Chicago Illinois. Data was collected from a total of 37 special needs
students in the multi-age fifth and sixth grades documenting that reading and vocabulary
More Problem Solving 7
contribute to the problem solving success challenge. A couple of vocabulary development ideas
used in their study include: concept maps, graphic organizers, and modified cloze activities.
The research by Blessman and Myszczak (2001) was intended to show vocabulary
growth. The information on the pre-test and post-test show an increase of about 15% for each
research site after vocabulary and comprehension activities were implemented. Students ranked
themselves as being highly knowledgeable about the vocabulary as opposed to initial responses
of average or low.
Rubenstein (2007) is a professor of education at the University of Michigan - Dearborn,
working with pre-service teachers and graduate students. In an informative article, she gives a
few strategies to teach vocabulary. One suggestion is that teachers use the etymology of
mathematical terms, and how they are related to everyday words. Another strategy is to draw a
picture and be sure to repeat the new terms while teaching vocabulary. Rubenstein shared a few
informative examples that illustrate how these strategies will help students make connections
among words to better understand them, rather than just memorize definitions. Another strategy
is to wait until after the concept has been introduced or discovered and then inform the students
on the name of the process or term.
As a mathematics teacher I had never given much thought to holding students
accountable for their mathematical language. As I emphasized vocabulary with hopes to improve
student achievement strategies implemented for this focused instruction come from Holden
(1999), Roti (2000), Blessman (2001) and Rubenstein (2007). If only one strategy is
implemented students will become bored; I want an entire box of strategies to pump up their
knowledge.
More Problem Solving 8
Communicating Mathematics
In an ever-changing world, methods and strategies used to communicate mathematics
continue to evolve as well. Many researchers use journals and written language to monitor
students’ progress. Yerushalmy (1997) notes that the use of The Algebra Sketchbook would
support many classroom situations and allow students to communicate through words, or graphs
or computers if they choose. Technology does not necessarily inhibit students’ abilities to
communicate mathematically. In fact technology often requires students to communicate more as
the computations are done by the calculators (Fletcher, 2003).
Teachers must continue to clear the line of communication in mathematics. “Language is
a major medium of teaching and learning mathematics; we serve students well when we support
them in learning mathematical language with meaning and fluency” (Rubenstein, 2007, p. 206).
Teachers must first patiently model mathematical language around students and allow students to
fully understand where each term fits within the concepts discussed. Students will do much
better in the mathematical world once they master the language.
Vocabulary is an essential element in the language of mathematics. Being able to
complete computations is meaningless without the ability to discuss its implication within a
situation. Regardless of including technology, students will benefit society more with an ability
to communicate mathematics.
Problem Solving
The National Council of Teacher of Mathematics (2000) continues to emphasize the
importance of problem solving. More students are being challenged with open-ended
mathematics questions to actively problem solve. Franke and Carey (1997) researched the
perception of 36 first graders about mathematics. After being given several problems students
More Problem Solving 9
were interviewed about what it means to be a good problem solver. The students expressed their
opinions that being good at mathematics is not just about getting the right solution the fastest.
Students refer to peers as good problem solvers because they used a good strategy and they
worked hard regardless of a correct answer. Only nine students even mentioned that the correct
solution was important. These ideas may be perceptions on the way because of reform
mathematics where the process is emphasized more than the outcome. “The children in this study
have helped us to see what it means to engage in mathematics, especially in classrooms where
problem solving is the focus of instruction” (Franke, 1997, p. 24). I know problem solving needs
to be a larger focus within my classroom and wonder what my classes will be like when that
happens.
After receiving more help with language comprehension and problem solving activities,
teachers of special education students observed a marked improvement with accuracy in problem
solving and doing so independently (Roti, et al., 2000). The Illinois Standards Achievement Test
has changed to emphasize vocabulary comprehension and problem solving including a detailed
written explanation including the used strategy (Blessman, 2001). Schoenberger and Liming
(2001) implemented their own problem solving acronym ODDE. This stands for Own Words,
Draw, Do work, Explain. Students are asked to use this to encourage them to show work and
then a table followed for them to explain the steps and why.
The first step to being a good problem solver includes doing the problem. The shift in
open-ended problem solving has become more evident and thorough explanations are expected
verbally and often written. Several teachers have their own algorithm to help students complete
the step to problem solving similar to Shoenberger and Liming (2001).
More Problem Solving 10
Conclusion
Overall, emphasizing vocabulary and the effect it has on problem solving has been found
to improve student learning. A student’s lower reading level may lower their achievement;
however, through vocabulary activities and clarification of meanings students will be able to
interpret word problems more successfully. My thought process is that my students need to
comprehend and communicate the overall question contained in a word problem. If necessary,
they need to translate alternatively between everyday word usage and mathematical terminology
as Kotsopoulos (2007) describes. Similarly, I have a list of important vocabulary words to
monitor and teach using strategies suggested from Holden (1997), Roti (2000), Schoenberger
(2001) and Rubenstein (2007). The age of students for my study is closely related to the students
form Fletcher‘s (2003) study. Even though many of the studies I referred to were for grades five
through seven, the information supplied is still very helpful for my research. The topics reading
comprehension, mathematics vocabulary, strategies for vocabulary acquisition, communicating
mathematics and problem solving are related to improve student performance on word problems.
I want students to solve word problems after emphasizing vocabulary with improved effort.
IV. PURPOSE STATEMENT
The purpose of my action research project was to observe if emphasizing vocabulary
would increase students’ ability to communicate mathematically and attempt word problems. In
my Algebra 1 and Algebra 2 classes, I examined variables including:
y the percentage of students in each course who complete
word problems on assignments /
tests
y the percentage of word problems proven correctly on tests
y the amount of vocabulary activities
More Problem Solving 11
y the amount of visual math vocabulary words surrounding the learning environment
These variables were addressed as I searched for answers to the following research questions:
y What will happen to the number of word problems students are willing to attempt after
receiving vocabulary instruction?
y What factors can students identify as reasons they do not attempt word problems?
y How does my teaching change as I emphasize vocabulary?
V. METHOD
For this action research, before a chapter would begin, I made a list of vocabulary terms
that were important or new for all students. As these words were introduced I would often point
out the words on the wall and use them at the beginning of class while I handed back corrected
and graded work. In Algebra 2, students were required to fill out vocabulary sheets a few times
and give and example with the definition.
At the beginning of the spring semester, January 4, 2008, I had students complete a
survey online with a likert scale for choices of Strongly Agree, Agree, Indifferent, Disagree, and
Strongly disagree and then again on April 11, 2008 with an additional question (Appendix A). I
collected information from interviews with two groups, one of three Algebra 1 students and the
other consisted of three Algebra 2 students with various abilities (Appendix E). The first
interview was on February 15, 2008 and the last on April 16, 2008.
Intermittently, I collected a rubric on the homework anonymously to have students
indicate how hard a word problem on their homework was, whether they completed the problem,
and check the reason(s) why or why not, with the option of listing another reason (Appendix B).
My goal was to have a weekly rubric, however with state standard testing, several days were
without homework. These assessments, graded as quizzes, were not included as a quiz in the
More Problem Solving 12
research as students must answer all questions or the computerized system would not submit
their answers. The first homework rubric was collected on January 10, 2008 and the last rubric
was on April 10, 2008. The rubrics were also used to tally word problem completion as other
assignments, quizzes and tests. In class, students were to write a journal once a month that
included a word problem; students were to write about their problem solving process (see
Appendix C for student journal format). At the bottom of the journal was a place to list three
recent vocabulary words. For some students this was the only time they used the word wall.
These collections were kept in separate folders for each piece and Algebra 1 was kept separate
from Algebra 2.
I kept a daily journal from January 3, 2008 through April 11, 2008 with a few prompts
where I noted what went well, poorly and if anything particularly interesting occurred. On
Fridays I tried to mention the highlights from the week. Had I written more fluidly daily rather
than making notes, my journal would be more cohesive (see Appendix D for journal prompts). I
often included differences in my teaching as something interesting, or unexpected remarks from
students.
I also used a spreadsheet to keep track of totals on the rubric choices being able to show
the two courses and combined, similar with the percentage completed and survey results
(Appendices F and G). This allowed me to see any chronological, categorical and combined
implications.
VI. FINDINGS
Throughout the research period I often had a question on the board for students when
they arrived. This would even include asking an Algebra 1 class to draw an inconsistent system
of lines. Time at the beginning of class was when students completed the rubric, before they
More Problem Solving 13
knew if the word problem was correct or not. After the tasks were addressed and verified, we
would begin to correct papers. Students corrected their own homework, and usually I had
students share answers as we go around the room. If three students in a row did not have an
answer, I would read the solution and emphasized that we may need to see that problem worked
out after the remaining answers were shared. I often assigned between 15 and 20 algebra
problems, but only graded four or five of them myself. Daily homework was worth five points
and for completed assignments students earn 60% for doing the assignment and I did not worry if
they corrected they papers accurately or not.
Students were notified of any quiz or test days in advance. A quiz consisted of five
problems worth two points a piece and possibly a bonus. Tests usually had 20 questions with one
or more bonus questions. Students were often given a quiz after homework had been corrected
and the homework due that day was not on the quiz.
Once everybody turned in the quiz, we discussed the next topic and may or may not have
assigned homework. During the discussion, I wrote out definitions on the board or overhead for
students to see and copy into their own notes or vocabulary sheet. These mathematical
vocabulary words were often associated with words in other context or built upon past
vocabulary and gestured towards the wall to point out the relations. Some vocabulary words
were defined or described orally. I showed the word on the word wall and arranged the words to
show connections with other vocabulary terms. After the needed words were shared, I showed
some problems and explained the process and steps included. Students then had an opportunity
to complete a couple exercises on their own and then get the homework assignment due the next
day.
Tests are given in a class period. Knowing some students are poor test takers and some
More Problem Solving 14
are poor test preparers, I normally allowed students to return until 4pm that day to complete their
tests if they wanted additional time. I almost always had all regularly handed in assignments
graded before class the following day so students received prompt individual feedback.
What will happen to the number of word problems students are willing to attempt
after receiving vocabulary instruction?
Students completed word problems most on quizzes, then on tests and least on
homework. The percentages found for completion in the graph below were 57.8% on daily
homework with a standard deviation of 22.3%, 95.9% on quizzes with a standard deviation of
only 3.75%, and 85.1% on tests with a standard deviation of 10.7%. I recorded a completion
percentage on a single question a total of 36 times. In Chapter 12 of Algebra 2, all questions on
the quizzes and test were word problems, so rather than report 35 problems I only recorded the
lowest on each and all were between 95% and 100% completed. The work for this chapter
showed increased completion on tests and quizzes while homework fluctuated from 50% to
100%. (See Appendix F for raw data)
Percenta
g
e of Completed Word
Problems
0
10
20
30
40
50
60
70
80
90
100
Homework Quiz Test
Percentage
More Problem Solving 15
In my journal on February 11, 2008 I noted “Some Algebra 2 students were complaining
about writing out the definition while others admitted to just guessing, knowing they will likely
get a point for trying on the test.” I noticed that often on the homework they would just leave an
assigned problem blank without even trying. In the student journals, often the same words were
listed as both confusing and helpful. Students still agreed that those were keywords, but not all
knew how to utilize the word to help solve the word problem. The vocabulary completion was
also sparse; even the students who suggested we needed more vocabulary never did that portion
of the journal.
Staying after school with a teacher and not being in trouble is unusual for many high
school students. During interviews some students appeared uncomfortable and did not really
offer many comments. In a first interview a student in Algebra 1 answered the question “Why do
you think that I am focusing on teaching math terms and vocabulary?” with “so we can better
understand the words when we are reading.” In the second interview another Algebra 1 student
answered, “so we have more options on a test.” Most students interviewed in Algebra 1 and
Algebra 2 mentioned that they only used the word wall when directly asked and they think
having the word wall will help them remember the words later on.
The overall influence of the vocabulary could not be seen in direct relation to word
problem completion. I expected to see a difference between the Algebra classes, since all the
word problems and concepts being taught were different. However, I did not find this. An
increase in word problem completion was expected, but was not substantially supported in my
findings.
What factors can students identify as reasons they do not attempt word problems?
More Problem Solving 16
A few findings presented themselves for reasons students do not attempt word problems.
My original idea was that students did not make time to complete homework assignments
because the word problems often occur towards the end. On the rubric this choice was added and
turned out to be the most popular option by Algebra 2 students. Overall many more students in
Algebra 1 marked that they did not know how to set up the problem. First I am going to talk
about students not being able to comprehend the problem, thus unable to set up or know how to
solve the problem.
In my journal on March 26, 2008, I noted a conversation with a male Algebra 2 student
who has intentions of entering the Navy if he improved his ASVAB scores.
While working with his recruiter they discovered that he has a lack of comprehension and
an inability to set up the equations. He is unable to solve problems with multiple
sentences but if the recruiter sets up the equation he can solve it fine.
While I have not officially heard about the Navy, I am thankful that somebody was able to take
more one on one time to work with him. This same situation concerning comprehension could be
true with several other students.
I noticed on the rubrics that often students marked that they did not understand the
question and they were unable to set it up. Looking at a handful of rubrics from April, I noticed
students marked that they did not like word problems and indicated the reason was that they were
confusing; however, they did not indicate which specific words were confusing, which was the
third choice on the rubric. The most commonly checked reason marked by any algebra student
was not knowing how to set problems up, 121 times out of a total of 423 rubrics marked the
problem was done attempted. Not knowing how to set up a problem was also the most common
More Problem Solving 17
among the Algebra1 students, accounting for 81 of the marks out of 260 unattempted Algebra 1
opportunities. This is exactly the factor I would hope going over vocabulary would address.
The pre and post survey data showed that the students understand knowing how to solve
word problems is important, as the top choice was agree on both surveys by,42 out of 90 students
in January and 34 out of 81 in April. Algebra 2 students remained to feel indifferent that
vocabulary helps them understand word problems better while the Algebra 1 students increase
agreement from 18 in 49 in January to only 19 in 46 in April. Several parts of the survey showed
students were indifferent to the questions and an overall decrease was common. I think part of
this could be that the first survey was conducted in the first two days of the semester and some
students may not remember their tendencies so soon after a break, while in April students were
able to draw on more recent experiences.
My other main contention that also accompanies the first research question is that
students do not always have or take the time to complete assignments and word problems. On a
rubric, a student marked that the problem was not done because he or she does not like word
problems. Beneath was a space to state why, here the reason was because they take too much
time. Not having enough time to complete assignments was the second most common reason
overall on the rubrics with 89 marks, 43 of them from Algebra 2 students.
The data collected from the surveys showed a drop in homework completion, and
attempting all word problems particularly. In January, 32% disagreed or strongly disagreed with
always attempting word problems and 52% said the same in April. To accompany this
information, in April 38 of 81 agreed or strongly agreed that assignments were completed and 59
said they had enough time on tests and 58 have enough time on quizzes. However more checked
strongly agree on quizzes. During the last interview with the Algebra 2 students, one boy who
More Problem Solving 18
had said previously in the year “We need to do vocabulary or something” said that paying
attention and actually doing the work would make him a better math student. Interestingly on the
student journals this student placed question marks on the lines for vocabulary and that was all.
Several students concurred that word problems are important and admitted to submitting
incomplete work. Poor reading comprehension inhibited at least one student from being able to
set up the problem. This was likely true for other students according to the rubric although not
specifically stated. Another common factor indicated by students was a time constraint for daily
assignments. Word problems are valuable, but unfortunately even those who realized the
importance did not possess all the skills needed to complete the process.
What happens to my teaching when I emphasize vocabulary?
As I emphasized vocabulary my teaching included more mathematical vocabulary and
more regularly. The increased technical terms were a byproduct of the word wall and definitions.
The installation of a word wall was useful for anticipatory sets and reviewing concepts. On
March 7, 2008 I noted in my journal “The students do look at the word wall or at least know it
exists. Yet few students know the meanings without referring to notes or the glossary.” Many
students did not notice the word wall for a few weeks and the words were not clearly visible to
the each student per his or her location and physical limitations of the classroom. The word wall
became more than a list of words and more of another place to express relations. A week later I
wrote that “more arranging and comparing vocabulary and concepts with the word wall.
Permutation / Combination. Probability / odds. Square of a sum / square of difference/ product of
a sum and a difference” for some comparison. A word wall was just another opportunity to
present concepts and show students important mathematical vocabulary.
More Problem Solving 19
The mathematical vocabulary was emphasized through multiple strategies. The Algebra 1
students took notes and made graphic organizers, while the Algebra 2 class had a vocabulary
sheet to turn in with definitions and examples to write for a grade. The Algebra 1 organizers
served as a student dictionary when the definitions and examples were written on the board. Prior
to my action research, I just gave the definition orally, if at all, and did not require students to
take notes. On March 25, 2008 “I had students each write their own definition for prime a the
beginning of the Algebra 1 classes” according to my teacher journal. Writing definitions forces
me to think more carefully about the specific definition I intend to use for various courses.
Vocabulary began to change how students and I communicated mathematics. In my
journal on January 11, 2008 I wrote “So far I have words on the walls and I find when I see them
I use them more readily and point them out as a visual reference of importance.” More precise
and accurate communication from me made me a better and more definite teacher. I constantly
found myself thinking of new connections between topics and debated if I should unveil the
relationship or allow my students the same opportunity to discover the connection on their own.
The topics do not need to be related for the concept to be learned and I am withholding the
additional information that could be a shortcut, more confusing for students, or a mnemonic link.
As a result, next year I will write definitions out for students and require regular
vocabulary work in some form. I have become a more technical and thorough teacher when I
emphasize vocabulary. My assessment of my teaching showed a positive influence through the
communication and understanding about becoming more informed of behind the scenes
happenings within the classroom.
More Problem Solving 20
VII. CONCLUSIONS
It appeared from the data that the amount of available time is related to word problem
completion. The complication with finding a direct relationship to vocabulary was that the
vocabulary words learned with a concept were not often the words contained in word problems.
Vocabulary may help students communicate mathematically with peers to make progress.
According to Schoenberger and Liming (2001), students must understand the vocabulary in order
to think about mathematical situations such as word problems. Another study, Nibbleink and
Hoover (1986) showed students with poor vocabulary could not identify necessary information. I
think of the senior boy trying to get into the Navy and his recruiter helped identify the reasoning
behind the scenes. Nibbleink and Hoover indicated that this student likely reads below grade
level. Through emphasized vocabulary and various activities, students understanding and use of
these terms should increase. Ideally high school graduates are more prepared and knowledgeable
based on experience and retained information.
Time and grading policy appeared to be influential factors of mathematics word problem
completion. Quizzes were shortest with the most time per question and guaranteed grade. Tests
were longer but students still know all problems will be graded and how many points would be
deducted for leaving a question blank. Students should also be able to reason that attempting a
problem will earn partial credit. Daily assignments did not guarantee each problem will be
graded and the involved students have little time around school activities and practices to
complete all homework in each class.
IX. IMPLICATIONS
More Problem Solving 21
As a teacher I may shorten assignments or give word problems the following day after
the process has been discussed. My thoughts are to continue to stress the importance of word
problems and keep assignments about the same, then perhaps students will work hard and meet
the challenges I place before them. I know I needed to implement strategies as suggested by
Rubenstein (2007) better with a more detailed plan. I anticipate keeping the word wall and
varying its usage. I like the grading policy but may state next year in the grading policy that one
word problem will likely be graded on each assignment. Students will share how they came up
with an answer so other students can see the process modeled by a peer, not just me. I also plan
to continue vocabulary sheets or puzzles to encourage more vocabulary usage. Reflecting upon
my teaching shows more areas for improvement than can honestly be tackled in a single year.
More Problem Solving 22
REFERENCES
Blessman, J., & Myszczak, B. (2001). Mathematics vocabulary and its effect on student
comprehension. Saint Xavier University& Skylight Professional Development.
(ERIC Document Reproducion Service No. ED455122).
Fletcher, M. (2003). Reading to learn concepts in mathematics: an action research project.
University of South Alabama. (ERIC Reproduction Service No.ED482001).
Franke, M, & Carey, D (1997). Young children's perception of mathematics in problem-solving
environments. Journal for Research in Mathematics Education, 28(1), 8-25.
Holden, W. (1999). Learning to learn: 15 vocabulary acquisition activities, tips and hints.
Modern English Teacher, 8(2), 42-47.
Kotsopoulos, D (2007). Mathematics discourse: “It’s like hearing a foreign language.”
Mathematics Teacher, 10(4), 301-305
National Council of Teachers of Mathematics. (2000). Principles and standards for school
mathematics, Reston, VA: Author.
Paul, D., Nibbelink, W., & Hoover, H. (1986). The effects of adjusting readability on the
difficulty of mathematics story problems. Journal for Research in Mathematics
Education 17(3), 163-171.
Roti, J., Trahey, C., & Zerafa, S. (2000). Improving student achievement in solving mathematical
word problems. Saint Xavier University & IRI/Skylight Professional Development.(ERIC
Reproduction Service No. ED 55923).
Rubenstein, R. (2007). Focused strategies for middle-grades mathematics vocabulary
development. Mathematics Teacher, 10(4), 200-207.
Schoenberger, K., & Liming, L. (2001). Improving students' mathematical thinking skills
through improved use of mathematics vocabulary and numerical operations. Saint Xavier
University and Skylight Professional Development. (ERIC Reproduction Service No.
ED455120).
Yerushalmy, M (1997). Mathematizing verbal descriptions of situations: A language to support
modeling. Cognition and Instruction 15(2), 207-264
More Problem Solving 23
Appendix A
Mark one box for each of the
following statements.
Strongly
Agree
Agree Indifferent Disagree Strongly
Disagree
I like math.
I am good at math
I often help explain math to other
students.
I complete all assignments.
It is important to know how to solve word
problems.
I always attempt all word problems.
I like having a word wall.
Using the word wall is helpful.
Learning vocabulary helps me do my
homework.
Learning more vocabulary helps my
understand word problems better.
I have enough time to complete the tests.
I have enough time to complete quizzes
(last survey only)
* conducted as an online survey with button choices for each answer
More Problem Solving 24
Appendix B
Rubric for word problem ___________
One a scale from 1 through 5, where 5 is the hardest, circle the difficulty
of this problem.
1 2 3 4 5
Did you complete this problem?
If not - check the reason(s) why.
I don’t like to do word problems. Why?
I did not understand what the problem was asking.
The words in the problem were too confusing?
The words I did not know were:
I did not know how to set up the problem.
I could not think of a way to solve the problem.
I did not have time or forgot.
Other (please explain):
More Problem Solving 25
Appendix C
Student Journal
(Leave a space for the problem to be pasted before copied.)
What is the main question or task to complete?
What words if any make this problem confusing to understand?
What words if any gave you an idea on how to solve the problem?
Describe the process you used to solve this problem?
List three mathematical words you learned this month, what each word means, and
an example of each word.
1.___________
2.___________
3____________
More Problem Solving 26
Appendix D
Teacher Journal Prompts
Research Questions:
y What will happen to the number of word problems students are willing to attempt after
receiving vocabulary instruction?
y What factors can students identify as reasons they do not attempt word problems?
Daily Journal:
I was pleased with the progress my algebra students are making because today:
I was displeased with the progress and learning in algebra today because:
I found it interesting when:
Weekly Journal
How do the incidents from daily journal relate to overall word problem completion?
How do they relate to the factors impairing students from problem solving?
What went well this week relate to my problem of practice?
What did I learn this week about vocabulary instruction and usage?
More Problem Solving 27
Appendix E
Student Interview
What part of math do you like the best?
Name a math skill you feel good about or enjoy.
Name a word used in math. Can you explain it to me?
Why do you think that I am focusing on teaching math terms and vocabulary?
Why do you think I have posted a lot of vocabulary words on the wall for math
class?
As I think about how much to focus on vocabulary next year in my math classes,
what advice would you give me? ( last interview only)
What helps you to become a better math student? Why? (last interview only)
More Problem Solving 28
Appendix F
Rubric data *red denotes the lowest of multiple word problem on one graded work*
Completion Completion
Alg 1 Alg 2
HW
83 44
64 24
69 79
75 100 57.78571429
24 60 22.33532329
43 50
23 71
55 60
54.5 61
22.64004038 23.071318
QUIZ
100 94
93 100
90
95 95.90909091
91 3.753785968
100
97
100
95
96.5 95.875
4.949747468 3.80058475
TEST
85 88
83 100
62 90 85.11111111
83 10.72898463
80
95
76.66666667 88.2
12.7410099 7.420691792
overall overall
66.077 81.7424
More Problem Solving 29
Appendix G
RUBRIC Factors
Totals
Algebra1
1. I don like word problems 4
2
4
8
5 8 3
34
2. I didn't understand the question. 7
5
13
14
17 8 3
67
3. Some words were confusing 1
0
2
4
1 3 0
11
4. I don't know how to set it up. 8
11
12
18
15 15 2
81
5. I could think of a way to solve it. 3
6
11
13
13 11 2
59
6. I did have time or didn't complete the
assignment. 4
4
4
6
6 16 8
48
other 6
1 4
Algebra 2
1. I don like word problems 4
8
12
4
2 6 0
36
2. I didn't understand the question. 2
1
11
2
1 1 0
18
3. Some words were confusing 0
1
2
1
0 0 0
4
4. I don't know how to set it up. 4
4
18
8
3 3 0
40
5. I could think of a way to solve it. 4
1
14
7
1 3 0
30
6. I did have time or didn't complete the
assignment. 8
12
6
5
5 7 0
43
other 6
Altogether
1. I don like word problems
70
2. I didn't understand the question.
85
3. Some words were confusing
15
4. I don't know how to set it up.
121
5. I could think of a way to solve it.
89
6. I did have time or didn't complete the assignment.
91
other
17
