Problem Posing and Problem Solving:
Costa Rica
A glimpse of culture difference in relation to Math
Zuleyma DeLaRosa
LAI 700 : Capstone Project
Professor: Dr. Son
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Introduction:
Problem posing is an significant element of the mathematics curriculum, and is
considered to be an vital part of mathematical doing (Brown &Walter). Problem posing includes
creating of new problems and questions intended at exploring a given situation as well as the
reformulation of a problem during the process of solving it (Silver, 1994). Providing students
with opportunities to pose their own problems can raise more distinct and flexible thinking,
improve students problem solving skills, extend their insight of mathematics and deepen and join
basic theories. As a student and future educator I wanted to focus my final paper and project on
the importance of problem posing and problem solving. However, while focusing on problem
posing and problem solving I wanted to further investigate incorporating culture. Throughout my
paper you will find many differences based on how math is taught in the U.S compared to Costa
Rica. During the summer of 2015 I participated in a program called Projects aboard and got the
opportunity to go to Costa Rica to teach Math in a school called, Escuela Cubujuqui. I was
teaching Math in Costa Rica for one full month and completed approximately 90 to 100 hours of
teaching. As I taught math at this school I found myself with the a challenge. The challenged I
faced while teaching math was being able to teach it in Spanish. Although I am a fluent speaker
in Spanish I was afraid of communicating the wrong information to the students. Nevertheless, I
surpassed my fear and was glad I was able to teach these students. Now I ask you what is
culture? Culture can be defined in many ways. Yet, dictionary.com defined culture as, “a
particular set of customs, morals, codes and traditions from a specific time and place.” Which
brings me to my research project, depending the time you were raised, taught and where you are
being taught determines many aspects in your educations. Throughout my paper you will
discover, why I choose this topic, what questions did I ask students, you will see students work,
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you will find literature review that expresses that math is taught different in all places, the
different types of teaching styles, and future suggestions for the addition of problem posing and
problem solving in teachers curriculum.
Method:
After taking the course LAI 545 Problem posing and problem solving I viewed math
differently. As a students I can honestly say that math was not my strongest subject, therefore I
always disliked math. However, when I think of math I think of numbers, symbols, letters that
represent something, equations, and rules for every operation you do. However, coming into the
course LAI 545, it took me out of that mindset I had about math and I saw a different perspective
of math. I remember coming into class my professor Dr. Son would always have a problem up
and we had to solve it. But the problems that were presented to us had no numbers, no rules had
to be apply, and no equation was needed. All she required us to do was to problem solve and to
not be afraid to pose a question of the question or the solution itself. As a result of this, my
interest sparked to further investigate about this topic. While taking this course I further my
investigation and did a project that focused on adults who were teaching students in afterschool.
The purpose of this specific project was to learn about teachers knowledge on what problem
solving and problem posing is and what do they know about Common Core. Once I concluded
that project I wanted to further investigate the knowledge of students in correlation to problem
posing and problem solving. In spite of this, I wanted to explore further and decided to do my
last project in Costa Rica. All finding that I will be writing about will be about my experience
teaching Math in Costa Rica. My goal for this project was to learn students perspective on math,
if they knew if there was a difference in problem posing and/or problem solving, and if they
knew what problem posing and problem solving meant.
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Research question:
To better investigate on the knowledge of the students I had some specific questions to
ask them which were, what is problem solving and problem posing? How much confidence do
you rate yourself when it comes to math (in a scale 1-10, 1 is the lowest and 1 0 being the
highest)? With asking these particular questions I will get a better insight on how the students
will be solving the math set of question I will be providing them with.
Findings:
Classrooms in Costa Rica have approximately twenty-seven to thirty students in a
classroom. Within each classrooms I was able to distinguish which students were high, average,
and low. For this study I had the opportunity to select six students who I wanted to focus on and
wanted those selected students to complete the problem posing and problem solving. Out of the
six students I selected, there was two high, two average, and two low. In the findings I will
provide you with you will see on the left hand corner on each worksheet there is a specific letter.
Letter A indicates for the students who are ranked high in their class when related to math, letter
B is for students who are average within the class, and letter C are students who show low
performance within the class. As mentioned above there were six students who completed the
worksheet give, out of the six students there were two girls and four boys. The A and B students
were boys and the C students were two girls.
To have a better understanding on the strategies these participants use to solve math
problems when completing an assignment I have created a worksheet for the participants to
complete. The questions used in the worksheet were questions students in class LAI 545 used in
their PowerPoints when presenting their topics. Some of the questions asked were related to
Math and some questions were not related to Math. By asking the students two different sets of
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questions would help me better understand their way of problem solving. Before students
completed the worksheet each of the students rated their confidence level for math. Students A
rated themselves higher compared to the rest of the students. Students A rated their confidence
level at a 7 and 8. Students B and C rated their confidence level at a 4, 5, and 6. Being able to see
their confidence level will give us a better understanding on how they performed when
responding to the questions I gave them. When giving the students the questions I had to
translate the questions into Spanish because Math in Costa Rica was taught in Spanish.
Nevertheless, I will be translating all the answers the students gave me in English below. The
questions on the worksheet were:
1. What does problem solving mean to you?
2. What does problem posing mean to you?
3. How would you rate your confidence level in regards to mathematics in a scale 1-10? (1
being the lowest & 10 being the highest)
Please solve the following problems:
4
A man painted all in black is wearing black. Black hood, black coat, black pants, black socks,
and black shoes. He walks down a black road with no street lamps. A black car comes toward
him with its lights off but stops in time. How did the driver see the man? Explain.
5
Scott the painter is going to paint the floors of 16 rooms. He is in room #1. He can go
through any door (see diagram). He cannot return to any room once he has painted it —
slow-drying paint! In what order should he paint the rooms? Obviously, #16 must be last.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
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6
7
If there are 7 people in a room, how many handshakes among different pairs of people can
occur? Explain.
What were easy in solving #7 and what were difficult?
Below you will find the participants answers to the questions of the worksheet
Student 1-A
Student 2-A
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Student 1-B
Student 2-B
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Student 1-C
Student 2-C
As we can see each participant that I gave the worksheet to had different opinions of what
problem solving and problem posing means to them. When asking students the questions what is
problem solving and problem posing mean to you, many of them did not know what to respond.
It took them a while to give me a response. A lot of them could not tell if there was a difference
between both. Students 1-A and student 2-A both said problem posing is something related to
operations and numbers in order to get the answer which is problem solving. Student 1-B and
student 2-B had different answers. Student 1-B said problem posing is “ using our minds to come
up with procedures to come to find an answers” and problem solving means, “solve the problem
that is being asked for multiple ways if possible.” Whereas, student 2-B believed problem posing
and problem solving was the same concept, solve the problem with numbers and operations.
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Lastly, Students 1-C and student 2-C responded the same way as student 1-B. however, when
students C were trying to write an answer they did not come up with the this answer on their own
they got help from student 1-B. We can conclude that in countries like Costa Rica problem
posing and problem solving is not given much attention. Seeing the way the students responded
to my research questions and seeing the way they solved each problem helped me detect how
they are thinking when problem solving. Furthermore, having the students solve these questions
also made realize the culture different between math in Costa Rica and the U.S.
Discussion and Implications:
The questions and statements each of the student asked while problem solving each of
these questions was interesting. Some questions that the students asked while problem solving
were, for question 4 participants stated if there was a black road it eliminates the possibility of it
being daytime therefore the person either had a flashlight or it can be daytime or it is a shadow.
For question 5 some questions the participants inquired were, can he go outside and walk around
the building? Can he go diagonally? Does he have to start from door 1? Is each room on a
different floor? For question 7 participants stated in solving this question visual helps, but it was
hard to make sure no one was repeating handshakes. So they decided to do is mathematically.
Observing the students thinking and solving process in Costa Rica made me appreciate
education in the U.S. I strongly believe being a student in the U.S we are expected to do well due
to all the resources we are provided with. Expectations as a student and teacher are very high in
the U.S. and I wish these types of expectations and requirements were enforced in countries like
Costa Rica. Being that Costa Rica does not have standards to follow or a curriculum such as
common core to follow I believe they do not have or follow any guidelines. What I mean by this
is they do branch off and explore other features of math. If problem posing and problem solving
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was given importance in Costa Rica or explained, students will have a better understanding of
mathematics when solving a fraction problem, word problem, or any other type of math problem.
Although there are some general categories of difference between cultures, there are
many ways that instruction can be designed or redesigned to become more culturally
sensitive. Adult educators can start to become more sensitive to cultural difference in
the classroom by first examining the cultural values that underlie their preferred
methods of teaching. Diversifying teaching methods should be a dynamic, interactive
process with learners that enriches all of adult learning (ERIC Development Team 6).
Literature Review:
In the article Culture and Math by Lili Tcheang, the author states, cultural differences
have been shown a number of different cognitive domains from vision, language, and music.
Mathematical understanding is another area that is an essential part of modern society and
because there are a permanent number of techniques in which many math operations can be
performed, it is also a contrary tool for cultural assessments. This argument studies the literature
on mathematical processing in agreement with culture, summarizing the brain areas involved
through several mathematical tasks. As a result, the author provides a functional similarities and
differences between cultures when performing different math tasks. The author expresses to its
readers that this information is beneficial to explore the probability of development of
mathematical skills, where different strategies may be relevant in agreement with culture. It also
contributes to the advancement of different math skills and the growing theory that functional
and behavioral studies must account for the cultural identity of their sample (Tcheang 54).
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The article Recognizing and Addressing Cultural Variations in the classrooms by
Carnegie Mellon discuss many topics that we can see happen in a classroom in a different
perspective. Within this article the author raise awareness about the types of challenges
international students face, provides examples of the kinds of issues that may affect students in
their courses, and offer suggestions based on strategies members of her own faculty have
successfully employed. But, my focus on her article was geared towards the classroom culture.
First, I wanted to discover how different can a classroom from the U.S and other countries be?
This article stated many great examples that you can find below. This article talks about the
difference between the teacher and student role, teaching styles, and student’s response to their
learning.
Classroom Culture:
U.S Education System
• In U.S. classrooms, the teacher’s role is to be an expert in their subject area. In addition
teachers are also seen as a coach, facilitator and a discussion leader (Mellon 6).
• In a U.S classroom students are usually expected to ask questions, specify areas of confusion,
and ask for examples to support their understanding. In some circumstances, students are
encouraged to debate their peers, challenge their professor’s ideas, etc (Mellon 6).
•There has been a greater importance in U.S. education on individual performance rather than
group work. Also, competitiveness, confidence, and honesty are promoted in U.S. classrooms
(Mellon 6).
Cultural Variations and their Implications
• In many countries, the teacher’s role is to communicate skilled knowledge and the student’s
role is to grasp it. Within these systems it would seem disrespectful for a learner to challenge an
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expert. Therefore, international students may be hesitant to question a teacher or to argue against
a published opinion (Mellon 7).
• In some cultures, students are expected to maintain a respectful silence in class. When
international students do not ask questions, the teacher may assume that they understand the
material. However, they do not (Mellon 7).
• In some cultures, group dynamics are developed in a more organized and sustained manner
than in the U.S., with greater value placed on interdependence and collaboration than on
individual performance (Mellon 7).
I have had the opportunity to teach in both settings, in the U.S and outside the country.
During my time teaching the U.S I have gotten the chance to work with kindergarten and fifth
grade students. Whereas, in the outside country I was teaching in, Costa Rica I was teaching
sixth grade Math and third and fourth grade English. I can say that both teaching experiences are
very different. Just like mentioned in the article Recognizing and Addressing Cultural Variations
the classroom culture setting were different. When teaching kindergarten and fifth grade in the
U.S. student were required to participated in discussion by asking questions, challenging teachers
theories, and if students were confused they were open about asking about clarification.
Furthermore, in fifth grade I saw a lot of encouraging students to do better for themselves being
that they were all applying to go to another school for sixth grade and teacher always emphasized
how competitive other students grades can be compared to theirs. Whereas, the classroom setting
in Costa Rica was different. The classroom instruction was teacher based. Being that it was
teacher based the lead teacher and I were at the front of the classroom majority of the time
lecturing to the students. In addition, when there was an adult in the room speaking students
would never interrupt the teacher. However, in Costa Rica students participated in discussion and
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asked question. But students never debated with a peer or a teacher about an answer. The had all
confidence in the teacher and their outlook on it was more of “the teacher is always right.”
Conclusion:
In conclusion, being able to do this project created a new outlook for me to understand. I
recognize the importance math all over. I understand that where ever I go education will be
different. However, as a future educator I should be able to extending my students thinking and
always incorporate students in my lesson. Some ways I can extend my students thinking and
involve them within a lesson is by, identifying and using students prior knowledge and
experience in planning programs and activities, design learning activities to motivate students
according to their interests and abilities, and identify students preferred learning styles and
promote the development of all learning styles. Overall, for someone who did not enjoy much
math when younger and as an adult I can say I feel more confident in the in part of helping and
involving problem posing and problem solving in my curriculum.
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Work Cited:
Ziegahn, L., & ERIC Clearinghouse on Adult, C. O. (2001). Considering Culture in the Selection
of Teaching Approaches for Adults. ERIC Digest.
Tcheang, L. (2014). Culture and Math. 55-65. http://dx.doi.org/10.1080/17588928.2013.838552
Mellon, C. (n.d.). Recognizing and Addressing Cultural Variations in the Classroom. 1-29.
Retrieved April 26, 2016.
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