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What Effects Does Collaboration Have on Students' Ability to Solve Math Word Problems?

Research into What Effect Does Technology and Collaboration Have on Primary Students' Ability to Attack Math Word Problems?

Video presentation of the first round of research.

Background:
At the close of the year, third grade students nationwide are expected to be mathematically proficient. California Common Core State Standards Mathematics Electronic Edition (2010, modified 2013) states, “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt.” Jumping into a solution is the response of most third-grade students.
Need:
Both National and State reported data supports the statement that Hispanic students and English Language Learners Enrolled more than 12 months in California schools are experiencing difficulty with communicating mathematical reasoning.

Data from the National Assessment states that 75% of grade four Hispanic students are not proficient, and 50 % of white students are not proficient. California data shows that only 30% of English Only students are above the standard for being able to think logically and express their thought in order to solve a problem. While only 10% of English Learners enrolled in U.S. schools for more than 12 months show proficiency.
National Assessment of Educational Progress (NAEP), 2015 for Mathematics

Rational:
This study examines the effect collaboration has on third grade students' ability to solve math problems. In the state of California, less than 13 percent of graduating third graders can think logically and express their thoughts in order to solve a math word problem Research sustains using project-based learning (PBL) as a vehicle to support collaboration, to close the achievement gap (Hixson, Ravitz, & Whisman, 2012). It also recommends the use of decentralized group discussion, to aid comprehension, as it is an active and constructive process (Peterson, 2016).   This study explores third grade student collaboration to solve a California Common Core aligned two-step math problem using Guided Language Acquisition Design (Be GLAD) strategies and a mathematical process method.
Quantitative data, for this study, showed no significant difference in using collaborative group work and Be GLAD strategies, for all students, including English Language Learners (ELL). However, qualitative data showed students had more opportunities to discuss understandings and misconceptions when they worked collaboratively.

Summary of Treatment Round 2::
Background:
In round 1, the teacher placed students in small collaborative groups. They were given a mathematical word problem supported by (stem open questions and statements) were also given a mathematical procedural model to help them analyze discuss and solve the math word problem. The students showed no significant improvement.

To improve performance, the teacher reflected on the different components of the lesson to discover what might be needed. First, an attempt to teach the procedural model with explanation for the steps to solve the problem was taught through Explicit Direct Instruction. Gestures were added to this instruction to help the students remember the steps. Then a math talk was conducted each day.

Through the math talks the teacher discovered that translating the problem and composing explanations was very difficult for the students. Next the teacher put the students in small instruction groups visiting two to three groups each day. The teacher soon discovered the students were not critically thinking because she was telling them what to do instead of using narrowing “Wh-“ questions to help guide their thinking. Through interviews with groups and individuals the teacher learned the students had difficulty looking at the question and deciphering the objective of the problem. The students also had difficulty deciding what was the important information in the problem. A suggestion by the math professional development staff to substitute boxes for the numbers was tried next. Unfortunately, the students still needed to be guided through the math procedure. Students continued to struggle with discussing when and why they were to use a particular mathematical operation or procedural step. The teacher then decided to employ strategies being suggested in her Learning Innovation master’s program. She narrowed the focus and added interactive technology.

Need:
Data analysis revealed that all students were able to input their ideas onto the project math poster.   At the beginning of the treatment 61% of all the students were able to explain their thinking of a common core word problem on a poster, at the end of the treatment 83% of all students were able to explain their thinking on the poster. Even though there was improvement in the students being able to explain problem solving strategies on the poster, data showed the class as a whole was not able to take what they learned and apply it to their posttest. However, scores for ELL students improved, 31% to 41%, on their individual exams, showing that there was some benefit for ELLs struggling with math concepts in a collaborative group. Pre-treatment feedback showed a positive attitude towards group work, however post-treatment feedback had decreased by six points.

Pre and Post Test

Rational:
At this juncture the teacher realized she needed to start with the understanding of the student's perceptions and then to move step by step in the process of solving math word problems. So, first step: Can the students successfully find the question in a math word problem and make it a statement with an unknown? It was found after teaching and practicing for half the year 50% of them could not, more research was required.

Further reading was required. (Pink,2006) Pink suggests using brain aptitudes to solve problems. In aptitudes of Story and Symphony, the math problem solver reads the problem, at first says, “To confusing” and shuts down, or jumps to a conclusion that makes no sense. But then the problem solver crosses into a new confusing world of words when looked at as a whole contains little meaning. What do these words mean? Symphony is the ability to take the parts and make a new comprehensible whole.   Thinking about these aptitudes led into reflections about the needs of the lesson design built to bridge the gap between presenter and student understanding. (Dervin,1992). Where are the “stops” the student is experiencing: How will they overcome barriers, and what is already understood about the material. What might be tried to alter understanding and then review, what helped toward new understanding? (Clark, 1999) stresses it is instructional methods and developing learning time to practice not media that impacts learning. In her description lesson design stages, task analysis helps provide suggestions to overcome barriers to learning. The learning objectives help alter student understanding. Develop from her Instructional Systems Design to plan, design, develop and evaluate stresses the importance to review what helped toward new understanding. She goes on to say “Because training is less than optimal, the software ends up underutilized and a portion sometimes a substantial portion-of the power of the system is never realized." (Carson,2007) Carson argues “one analyzes the meaning of problem solving, the knowledge base and the transfer of that knowledge are the most essential elements in solving problems” supported the idea that students must have appropriate background knowledge to be able to think critically and participate in problems solving. (Alberta Education, 2015) discusses the importance of building new information on what is known for individuals and groups of students. “To gradually shift the responsibility of learning from the teacher to the student, scaffolded building on the understanding that students learn in many ways, is built on known level of knowledge the student possesses and provides differentiated instruction to help support students in crossing the learning gap. To maximize student success using a technology scaffold must be combined with effective instruction to design learning environments to support the success of every student.”

This research provided the teacher with a new course of action. Providing the students with interactive video forms, and games to scaffold and support background knowledge of vocabulary and skills needed to turn a question sentence into a statement sentence required differentiated lessons, the lesson design morphed into a project, and asking students to design their own explanations of how they solved a problem to reach their audience, other grade level members. Math problems must be comprehensible to all various pathways for solution. Lessons took on multiple dimensions: a.) used critical thinking skills in collaboration with peers, b.) provided skill and vocabulary support so each member of the group participated equally, and c.) provided a platform for students to contribute to a math presentation project and explain there thinking process.

Treatment:
The students were given a pre and post-tests for: Vocabulary Interrogative Test, Make a Question Sentence into a Statement Sentence, and Solve a Two-step Grade Level Math Word Problem Using Information from a Graph. The students then watched short videos about interrogatives and the skill “How to turn a question sentence into a statement sentence.” These videos were created by the teacher using PowerPoint animation and embedded into google forms. These forms contained questions to help the student retain information from the videos. The students also practiced learning interrogative vocabulary playing games created on google slides: flashcards, and a simple leveling up game.   The teacher then used the prior knowledge of the videos and direct instruction to teach a math procedural model to solve math word problems. After reviewing guidelines and assigning roles for group interactions the students then each drew a picture for each step of their math plan to solve the problem. With support from their peers each student then scripted their drawing. The drawing and scripts were then used to create a screen-cast of each group’s solution to the math word problem.

Results:
Adding technology to the driving question, What Effects Does Collaboration Have on Students' Ability to Solve Math Word Problems?, promoted many questions: How does the ability of making a question into a statement effect the students ability to answer a grade level math word problem? Can the students translate the interrogative in a question and add an unknown to make a question a statement? To what degree would an interactive tutorial with an avatar support students? Do teacher created games support understanding of interrogatives?   How do students, with background information and who have worked collaboratively completing a script on Google Forms and Screen cast, perform in their ability to independently explain math word problems on an exam? Is there a difference in the effects for English Only and English Language Learners?

To conceptualize, research, narrow the focus it is helpful for students to turn the question sentence in a math word problem into a statement sentence with an unknown. At the beginning of the research 52% of EO (English Only) students and 38% of ELL (English Language Learners) were successful. In order to make the question comprehensible the student must identify the subject of his inquiry and therefore be able to translate the interrogative. There was not a significant difference between EO and ELL the average student got 65% correct.
Creating an interactive avatar lesson was introduced. (Clark, 1999) “Adding graphics to the lesson shows increases student interest and comprehension.” Would these lessons make the information more accessible to all students? After completing the lesson EO students improved by 20 % points where as there was no significant change for ELL's.
Allowing time for appropriate practice supports student working memory, hence two types of games were introduced for practice. One game was a single player level game and the other a partner game winner has the most points. These activities resulted in not a significant improvement for EO's; however, ELL students increased by 20 points. Both the EO and ELL students’ average of percentage correct was 85%. After these procedures to what effect did understanding the interrogative in a question play into being able to translate the question into a statement with an unknown? EO students’ ability percentage points increased by 16%, and ELL students increased 23% points.
Because ELL students were able were able to make significant improvement with the interactive interrogative lesson would this support their ability to turn a question into a statement? The student response for their independent work on their interactive avatar lesson showed a 5% increase for EO's but a 10% increase for ELL's. How would this affect their individual exams? EO students made no significant increase, however, ELL's test results increased by 9% points in their independent ability to translate a question into a statement with an unknown.
Collaboration from the first round of treatment showed no significant increase for EO students, but ELL correct responses increased 31 to 41 percent, an increase of 10 % points. After using technology lessons making a question into a statement the students made no significant improvement discussing how to solve a grade level math word problem on an independent written exam. However all the students successfully completed their portion of the math process and contributed in decentralized groups to create a screen-cast of how to solve a grade level two step word problem.

Survey

The students were then given an independent exam after screen-cast lessons and showed EO students had increased 48 % to 74 % and ELL students had increased 31% to 76% in their ability to independently discuss how to solve a grade level math problem on a paper exam.
Surveys indicated that students enjoyed playing computer games with another student 20% more than playing alone. ELL students responded that they preferred games and teacher discussions to avatar tutorials. When asked what helped them the most student response both ELL and EO students equally responded, half the class liked group work with teacher support, and the other half preferred working with technology.

Conclusion:
To meet the third grade national standard, students must be able to effectively argue their mathematical thinking. Research supports that students who work together, to create a product, engage with the content, as well as one another, form deeper understandings, and thereby increase their ability to communicate their mathematical reasoning. Research also sustains using graphics, gaming, and project based learning as a vehicle to support collaboration to close the achievement gap. The teacher has sought to explore to what effect collaboration and technology had on students’ ability to solve math word problems, using Be Glad strategies and explicit teaching of a math process method, in addition to an interactive avatar tutorial and teacher created games to support background knowledge. Would this support students’ ability complete a word problem collaboratively on a slide deck and then screen-casting their work explaining how they reached their conclusion. Data gathered showed that adding scripting to produce a screen-cast supported English Language Learners’ ability to explain steps needed to solve a math word problem.

Capstone Poster

The Journey: An Annotated Bibliography

An account of the past 30 years in education and how it continues to keep the poor poor. This book inspired to teach: click on SCRIB

Start with a math plan linked to article by Carson, J. (2007). A Problem With Problem Solving: Teaching Thinking Without Teaching Knowledge.

$Picture$

Research shows positive results for students working together. The Effect of Cooperative Learning Strategies on Elementary Students' Science Achievement and Social Skills in Kuwait, Ali Ebrahim

Students needed rules and roles to be productive. Several ideas from Pinterest.

It was helpful to show student short clip of how to work cooperatively. This site also suggested roles and group formations. Edutopia: Oracy in the Classroom

Students worked successfully in groups however they were experiencing difficulties explaining their thinking. Liu and Xin (2017) used translating mathematical sentences to explain their reasoning.

Students continued to have difficulties discussing word problems. Perhaps Math Talks would help. Instructional resources were gathered from www.youcubed.org.

Began thinking about creating a student project incorporating technology. Projects That Have Been Put to the Test By Anne-Lise Halvorsen

More research about brain research and lesson design.

Screen-cast about how our memory works. Reinforcement needed within 90 minutes.

Brenda Dervin in her article “From the Mind’s Eye of the User: The Sense-making Qualitative-quantitative Methodology” , Ruth Clark in her book Developing Technical Training, Using Differentiated Instruction to Support All Learners, Elberta Education 2015

1999, Dervin Drawing explaining the learning gap.

Design Map about Ruth Clark's Developing Technical Training, 1999 Click on map for Clark's Virtual Classroom

Published on Jan 30, 2015 Watch Alberta Education’s the importance of including all students

Now it was time to design tools.

Now it was time to make games in Google, this youtube was very helpful as it had adaptable templets.

Research and Ideas

Literature Review For Treatment 1:

Indications from research show that students’ productivity in cooperative learning settings is higher than in teacher-centered situations. Najmonnisa and Ismail Saad (2017) conducted a 13 week quantitative and Quasi-experimental research designed to report the effects of cooperative learning method on students’ academic performance in a Pakistani classroom. The research design included two groups one that received treatment and was taught with cooperative learning and a control group that was left untreated, taught a lecture method. This research supported the success of cooperative learning in the improvement of scientific knowledge and skills such as labeling, inferring, prediction, explanation, judgmental and reasoning, the same skills needed in solving math problems.
Another study that speaks to the importance and success of cooperative learning such that students will show positive interdependence, individual accountability, shared ownership, and the effectiveness in the group process (Ebrahim, 2010). In this study teachers were asked to utilize both teaching strategies; one randomly selected class received teacher-centered instruction and the other class received cooperative learning instruction. researcher-designed achievement social skills were determined by a researcher-designed survey. The fundamental findings of these studies indicated that students’ productivity in cooperative learning settings is higher than in teacher-centered situations.
Studies also support comprehension as an active and constructive process. Benefits of decentralized group discussions are: the ability for students to take risks, to make errors, and to refine previously held ideas. However, it is recommended that students should be debriefed after meetings in which the teacher might guide the students into deeper understandings (Peterson, 2016). This study explored the positives and negatives of decentralized small group discussion in a multiage (3rd/4th) grade classroom. Data was analyzed using a combination of constant comparative methods and a micro analysis of talk drawing on traditions of sociolinguistics.
Researcher and teachers in another study (Banes, Lopez, Skubal, & Perfecto, 2017) based upon three classrooms, found that all students were able to clearly explain their math concepts both in oral and written formats, this included bilingual learners and students who had math difficulties . A student group-created poster is a vehicle that might support student discussion and analysis. Where in, students have the opportunity to debate extra information, negotiate what counts as “Proof”, and enter into class discussions reflecting on the products.
However, students struggle to put their ideas into words, especially second language speakers and students with learning difficulties. In this area, it is possible that conversational repair could give teachers tools to meaningfully intervene and support student connections. Liu and Xin (2017) used translating mathematical sentences as a vehicle to support students in an implicit-explicit continuum to be able to explain their reasoning. This was done by the teacher asking questions, which translated mathematical sentences, and helped students with their mathematical reasoning and problem solving. There was an immediate increase in their problem solving performance. Asking students questions, that scaffolded the complexity of the word problem, helped the students to explain and justify their reasoning.
Students also experience difficulties in finding strategies to attack a problem. They need direct guided instruction to help them build cognitive strategies. Morin, Watson, Hester, & Raver (2017) conducted videotaped sessions and a social validity survey of 5 students who were given 8 word problems representing 8 levels of complexity. They found that direct instruction of a mathematical method model helps students build cognitive strategies. These strategies included rewriting the question as an answer, and discussing a plan of action.
In conclusion, research advocates the use of decentralized groups to support students’ opportunities to translate the problem into meaningful concepts, especially for second language learners. A single product for a small group requires the students to feel individually responsible to make proposals, to argue concepts and to negotiate for meaning by explaining to themselves and others a solution pathway. The role of the teacher is to explicitly teach a problem solving method and then to listen carefully ask scaffolded questions to help students to listen, discover misconceptions and build upon their own understandings. This study researches the effect collaboration has on third grade students' ability to solve math problems.

Literature Review For Treatment 2:

Understanding of the student's perceptions and then to move step by step in the process of solving math word problems was necessary. So, first step: Can the students successfully find the question in a math word problem and make it a statement with an unknown? It was found after teaching and practicing for half the year 50% of them could not, more research was required.
Daniel Pink’s, A Whole New Mind, supports math word problems as being reflections of daily life to be communicated, through words, pictures, patterns, and symbols. Could these activities and brain research to help students become better problem solvers? The left side of our brain is the logic center. This is important player in finding solutions, but alone it has not made students successful problem solvers. Practices that must added lessons are the 6 aptitudes described by Daniel Pink: Design, Story, Symphony, Empathy, Play, Meaning, and Importance. The math problem solver reads the problem, at first says, “To confusing” and shuts down, or jumps to a conclusion that makes no sense. But then the problem solver crosses into a new confusing world of words when looked at as a whole contains little meaning. What do these words mean? However, the problem solver is not alone; in his/her collaborative group they will examine the problem by definition, by prior knowledge. The student asks, “What am I looking for?” "How is this situation related to others like it." How can this be modeled, acted out, or drawn? What patterns exist?" “What actions must be carried out?" “What symbols will be used?" But along the way the aptitude of Symphony is built with the help of his collaborative group with prompting questions, What do you know?, How did you find this?, and Why do you think? Symphony is the ability to take the parts and make a new comprehensible whole. Eventually the students find the end in of the maze and find the solution. The “AHA!” moment.

Thinking about these aptitudes led into reflections of the student as the end-user of the lesson design. This theory is also supported by Brenda Dervin in her article “From the Mind’s Eye of the User: The Sense-making Qualitative-quantitative Methodology” focuses on the learning gap. “… by defining and gap bridging we allow to emerge for examination human flexibilities and rigidities and allow the possibility that both are amenable to systematic analysis.” Dervin examines the gap of understanding between the end user and the presenter, it is important to bridge this gap looking at what path the student is trying to use. Where are the “stops” the student is experiencing: How will they overcome barriers, and what is already understood about the material. What might be tried to alter understanding and then review, what helped toward new understanding?

Ruth Clark in her book Developing Technical Training stresses it is instructional methods and developing leaning time to practice not media that impacts learning. In her description lesson design stages, task analysis helps provide suggestions to overcome barriers to learning. The learning objectives help alter student understanding. Develop from her Instructional Systems Design to plan, design, develop and evaluate stresses the importance to review what helped toward new understanding. She goes on to say “Because training is less than optimal, the software ends up underutilized and a portion sometimes a substantial portion-of the power of the system is never realized."

“A Problem With Problem Solving: Teaching Thinking Without Teaching Knowledge” by Jamin Carson argues “one analyzes the meaning of problem solving, the knowledge base and the transfer of that knowledge are the most essential elements in solving problems” supported the idea that students must have appropriate background knowledge to be able to think critically and participate in problems solving.

Enlightening Articles:

Carson, J. (2007). A Problem With Problem Solving: Teaching Thinking Without Teachng Knowledge. Mathematics Educator, Vol. 17, No. 2 7-14.

Thinking skills teachers use to teach students how to think for problem based learning are: critical thinking skills, creative thinking skills, decision making, conceptualizing, and information processing. This article discusses the idea that a knowledge base is an essential element in solving problems. It also includes steps in problem solving by John Dewey 1933, Stephen Krulik and Jesse Rudnick 1980 and George Polya 1988.

Design Process

Support and Next Steps