Resolucion de problemas matematicos online dating

APMO - Olimpiada Mexicana de Matemáticas

resolucion de problemas matematicos online dating

Evaluación on-line del proceso de resolución de problemas matemáticos en . To date however, this method has neither been applied to the analysis of the. In case you haven't heard, there's an online dating site called Farmers Only, which boasts the tagline, "City folks just don't get it!" (By the way, that tagline's totally. Creatividad e ingenio para la resolución de problemas . a written legend, warning the students not to discuss the problems over the internet until that date.

Most studies have been based on applying standardized measures such as questionnaires or structured interviews; this kind of measures involves asking students about how they solve a problem or the extent to which they use different strategies.

Additionally, students are also asked about different situations in which they would use or not use a specific strategy or what approximation would be the best in each case. Students' responses to the metacognitive questions are scored depending on the quality of the response and a total score is calculated.

In response to this, Veenman established the distinction between off-line and on-line methods in the assessment of strategy use and learning. Off-line methods refer to questionnaires and interviews which are administered either before or after task performance, while on-line methods concern measurements taken concurrent to task performance, such as Think - aloud or Triple Task procedures.

These measures may be especially useful to provide data about student reasoning abilities during problem - solving activities. In Think - aloud protocols Rosenzweig et al. The usefulness of these procedures lie in the fact that they provide access to students' short-term memory abilities, which reflects cognitive processing during task completion. This approach allows the researcher to obtain accurate information about metacognitive skills and strategies while students are asked to simply verbalize what they are thinking at each moment.

After transcription and coding, undirected verbalizations are recognized as valid expressions of the students' cognitive and metacognitive processes. Although the present study focuses on the use of Triple Task procedures, a description of both methods is provided below: The Double Task procedure provides information about the cognitive effort engaged in higher - order cognitive tasks, such as comprehension or text production.

Participants are asked to perform concurrently a primary task and a secondary probe task. Reaction time RT in this dual - task situation is compared with a control condition when the probe is responded to as a single task. The degree of interference in RT IRT caused by the primary task provides a measure of the amount of cognitive effort designated to composition or another cognitive task. However, although widely used, this measure does not provide information about the process that underlies the cognitive task under consideration.

It is the Triple Task procedure which provides additional information about the temporal organization and the cognitive processes underlying a cognitive activity by adding a third task, consisting of asking students for an immediate directed introspection after each tone's detection.

Students have to categorize their thoughts at the moment the tone is presented. Thus, in Triple Task studies students perform: For this last task, participants are trained in direct retrospection in order to better identify and report the cognitive processes present at each moment.

As a measure of the process, the Triple Task method can be differentiated from Think - aloud protocols in the following aspects: To date however, this method has neither been applied to the analysis of the processes underlying mathematical problem - solving, nor from the point of view of investigating the metacognitive skills involved in these tasks.

Additionally, as happens with Think - aloud protocols, most Triple Task studies have been conducted with small sample sizes, mainly due to their own methodology feautures, which make them less economic to implement. One of the novelties of this method is the introduction of a new system of categories to analyze student processes during problem solving. Identifying potential problems, Defining and representing the problem, Exploring possible strategies, Acting on those strategies, and Looking back and evaluating the effects of those activities.

A more detailed description of the assessment process and this tool, which was administered to students from fifth and sixth grade belonging to 12 private and state schools in Asturias Northern Spainis provided in the method section.

The main aim of this study was to analyze the usefulness of TTPM as a measure of the process during the performance of two mathematical problems of varying difficulty. Specifically, this study sought to answer the following questions: Participants The study involved students from fifth and sixth grade students from 12 private and state primary schools in northern Spain Mean age: Students belonged to 32 different classrooms.

Gender distribution was balanced. Of the total sample, students Gender and level fifth or sixth grade were taken into account as potential mediating variables in subsequent analyses. Sample selection was made through convenience or accessibility procedures. Students volunteered for the study and presented informed consent from their parents. This book provides a systematic review of the characteristics that define a good problem solver, while proposing strategies and activities to develop these skills, mainly based on mathematical reasoning.

Tasks differ in the amount of information to be processed, the number of associations presented and the number of parameters to calculate. It consists in the following: At this point students are asked to categorize their activities or thoughts. In order to help students, categorize these processes, students are provided with a category system see Table I.

Nevertheless, previous research indicates that such unrelated processes are generally very scarce Olive et al. The eight proposed processes are also organized into three, higher - level categories corresponding to SRL phases: Planning, Execution and Revision.

Table I shows the category system used for students to categorize their processes during the task, based on the correspondence between the stages and phases involved in both SRL and IDEAL models.

Procedure The study was conducted in accordance with The Helsinki Declaration of the World Medical Association Williams,which reflects the ethical principles for research involving humans. Participants were tested colectivelly within a 45 - minute time - frame. A maximum of 20 participants were tested at a time.

The first phase consisted of training students to familiarize them with the system of categories and the assessment procedure. After training, students performed a category recognition test consisting of 12 multiple - choice items with four alternatives. Students were asked to indicate the category that best expressed each proposed activity e. Once the system of categories was undertood, students were informed that they would occasionally hear a tone coming from the computer at varing intervals, and they were instructed to quickly react to every tone by clicking on the computer mouse with their dominant hand.

This tone was presented in a randomized interval of seconds. Then they were informed that this same sound signal would appear while they tried to solve the tasks. They were asked to choose the category that best represented what they were doing in each moment. The tone was presened in a randomized interval of seconds.

Concurrent to the tone, a pop-up appeared on the computer screen. It showed a box with the category system. Students were able to select a category with a mouse-click. Mathematical problems were provided on paper.

Students could use that paper to write whatever they needed, with the condition that they had to write their answer on the paper when they finished the task.

As data were collected from individual students simultanteoulsy, head - phones were provided in order that other students were not disturbed. Data collection was implemented through Moodle platform https: A special module was created on the platform, that hosted the evaluation procedure and stored data. In order to acoomplish that, a multidisciplinary team, including psychologists, teachers, and a computer engineer responsible for all technical issues collaborated during the study.

Students accessed this platform through an individual username and password in order to guarantee their anonymity. Once data were obtained and stored, they were automatically transferred to an Excel file for subsequent processing.

Process variables were based on frequency counts. Frequency of each sub-process or category was established by dividing the frequency of election of that category by the total number of elections done across categories. These frequency counts were then transformed into percentages by multiplying the quotient by Finally, students' achievement in the mathematical tasks was established in terms of success 1 or failure 0 according to the answers given on paper.

Given the main aims of this study, centered in the process, RT's as a meaure of effort were not taken into account for data analyses. Data analyses Ex - post - facto descriptive and comparative design was used in this study. After describing the profile of process followed by the total group in each task, Multivariate Analysis of Covariance MANCOVA analyses with process variables 8 categories and 3 higher - level categories as dependent variables, and gender and level as covariates, were conducted in order to investigate differences between groups with different achievement.

Tasks were analysed separately in order to determine the importance of task difficulty as a factor explaining these differences. Data were analyzed with SPSS Student problem - solving process In order to demonstrate if a student's problem-solving process responds to SRL phases, Figure 1 shows the profile of the process followed by students in Tasks 1 and 2.

This profile indicates similar processes for both tasks, characterized by a higher frequency of selected categories in planning and execution phases. The means Table II indicated a percentage of With respect to the revision phase, mean percentages of categories reported within this phase were It must be noted in this case the high means found in the planning phase even above those found in the execution phase.

This is because the planning phase consists of four sub-processes or categories, while the other phases comprise two. Figura 1 Process profile of the total sample. Tasks 1 and 2. Group - compositions revealed the presence of a high proportion of students solving the mathematical problems unsuccessfully. Specifically, students As one of the aims of this study was to know whether there were differences between tasks with varying difficulty, separate analyses for each task were conducted.

For the first task, means in Table III indicated a trend to plan more, and to execute and review less, in the Group 1 success. As happened with planning, this sub-process was more frequently reported by students who successfully solved the task. Task 1 With respect to the second task, the means in Table IV showed a different pattern of results, with students who successfully solved the problem reporting using less sub-processes related to planning, and more related to the execution and revision phases.

These differences were found in those categories or sub-processes within the planning phase: Means revealed that students who successfully solved the task Group 1 reported reading, recalling similar problems, and thinking about solutions less frequently than the other group. As with the first task, successful students also reported using representation strategies i.

In this context, the main aim of this study was to analyse the usefulness of a new assessment tool based on the Triple Task procedure and designed to assess the metacognitive and self - regulated processes shown by the fifth and sixth grade students during the performance of two mathematical problems of varying difficulty.

Specifically, this study tried to answer these questions: Do students follow Self - Regulated Learning stages while they try to solve mathematical problems? Global results indicated the presence of important differences among processes followed by students, as indicated by the high standard deviations.

This variability was even higher in the categories or sub-processes less frequently reported by students in general: The pattern of results was similar in both tasks, and was characterized by a lack of evaluation strategies. However, sub-processes related to Planning and Execution phases were the most frequently reported, respectively. However, despite the fact that these results could indicate that once students properly planned an activity, making mistakes became less likely and reviewing activities less necessary, students' achievements in both tasks revealed a high proportion of failure.

This indicated that planning strategies were not effective enough. In fact, an analysis of the sub-processes involved in the planning phase revealed that thinking about solutions and reading were the most frequently reported sub-processes within planning, while the use of potentially more useful strategies such as information representation and organization were less frequent among students.

This result could indicate a trend to use passive solving strategies or even comprehension difficulties. Are there differences in the processes followed by students with different achievements in the tasks? Analyses revealed the existence of statistically significant differences between groups. These differences were located in the subprocess of drawing or summarizing in Problem 1, while significant differences were found in all the sub-process within the planning phase in Problem 2.

The existence of more significant differences in this second problem could be related to its characteristics i. Thus, this task may result more difficult, suggesting a more important role of planning strategies when problem difficulty and demands increase. Regarding the pattern of differences, students who successfully solved the tasks tended to draw and summarize more, but they recalled similar problems, read and thought about solutions proportionally less than those who failed to solve the tasks.

These results are consistent with the statement above about the effectiveness of planning strategies, and suggest the use of more active processes by students with high achievement.

In this sense, the strategy that showed to be effective in both tasks was drawing or summarizing i. An example of graphical representation, made by a participant in this study, is shown in Figure 2. Figura 2 Example of students' answers in the second task The use of graphic representations supposses an important part of planning strategies.

As Montague and othersp. In fact, Abdullah and others showed in their study that when the teaching approaches encourage students to apply thinking strategies through using visual representation, students are able to gain a better conceptual understanding and eventually improve their mathematics achievement.

They attributed this effect to a more active involvement of students in their learning process. However, representation is not only a matter of copying what one sees. As the example above shows, it involves a process of personal re-organization, inventing or adapting conventions of a representational system for the purpose at hand Stylianou, Are there differences between tasks with varying difficulty?

Although differences in the main phases of planning, execution and review were not statistically significant, analyses revealed the existence of significant differences in the sub-process involved in planning, separately. As a measure of the process, the Triple Task method can be differentiated from Think - aloud protocols in the following aspects: To date however, this method has neither been applied to the analysis of the processes underlying mathematical problem - solving, nor from the point of view of investigating the metacognitive skills involved in these tasks.

Additionally, as happens with Think - aloud protocols, most Triple Task studies have been conducted with small sample sizes, mainly due to their own methodology feautures, which make them less economic to implement.

One of the novelties of this method is the introduction of a new system of categories to analyze student processes during problem solving. Identifying potential problems, Defining and representing the problem, Exploring possible strategies, Acting on those strategies, and Looking back and evaluating the effects of those activities. A more detailed description of the assessment process and this tool, which was administered to students from fifth and sixth grade belonging to 12 private and state schools in Asturias Northern Spainis provided in the method section.

The main aim of this study was to analyze the usefulness of TTPM as a measure of the process during the performance of two mathematical problems of varying difficulty. Specifically, this study sought to answer the following questions: Participants The study involved students from fifth and sixth grade students from 12 private and state primary schools in northern Spain Mean age: Students belonged to 32 different classrooms. Gender distribution was balanced.

Of the total sample, students Gender and level fifth or sixth grade were taken into account as potential mediating variables in subsequent analyses. Sample selection was made through convenience or accessibility procedures. Students volunteered for the study and presented informed consent from their parents.

This book provides a systematic review of the characteristics that define a good problem solver, while proposing strategies and activities to develop these skills, mainly based on mathematical reasoning.

Tasks differ in the amount of information to be processed, the number of associations presented and the number of parameters to calculate. It consists in the following: At this point students are asked to categorize their activities or thoughts. In order to help students, categorize these processes, students are provided with a category system see Table I. They have to indicate by mouse - click which of nine the categories reading, drawing or summarizing, recalling similar problems, thinking about a solution, mental calculation, writing, reviewing, correcting mistakes, or "other" best describes the processes in which they are involved when the tone is presented.

The category called "other" was incorporated to gather all those thoughts or actions unrelated to the mathematical task e. Nevertheless, previous research indicates that such unrelated processes are generally very scarce Olive et al. The eight proposed processes are also organized into three, higher - level categories corresponding to SRL phases: Planning, Execution and Revision.

Table I shows the category system used for students to categorize their processes during the task, based on the correspondence between the stages and phases involved in both SRL and IDEAL models. Procedure The study was conducted in accordance with The Helsinki Declaration of the World Medical Association Williams,which reflects the ethical principles for research involving humans.

Participants were tested colectivelly within a 45 - minute time - frame.

  • La Resolucion de Problemas Matematicos (English, Spanish, Paperback)
  • Asian Pacific Mathemathics Olympiad

A maximum of 20 participants were tested at a time. The first phase consisted of training students to familiarize them with the system of categories and the assessment procedure. After training, students performed a category recognition test consisting of 12 multiple - choice items with four alternatives.

Students were asked to indicate the category that best expressed each proposed activity e. Once the system of categories was undertood, students were informed that they would occasionally hear a tone coming from the computer at varing intervals, and they were instructed to quickly react to every tone by clicking on the computer mouse with their dominant hand. This tone was presented in a randomized interval of seconds.

Then they were informed that this same sound signal would appear while they tried to solve the tasks. They were asked to choose the category that best represented what they were doing in each moment.

Instituto de Matemática Interdisciplinar

The tone was presened in a randomized interval of seconds. Concurrent to the tone, a pop-up appeared on the computer screen. It showed a box with the category system. Students were able to select a category with a mouse-click. Mathematical problems were provided on paper. Students could use that paper to write whatever they needed, with the condition that they had to write their answer on the paper when they finished the task.

As data were collected from individual students simultanteoulsy, head - phones were provided in order that other students were not disturbed. Data collection was implemented through Moodle platform https: A special module was created on the platform, that hosted the evaluation procedure and stored data.

In order to acoomplish that, a multidisciplinary team, including psychologists, teachers, and a computer engineer responsible for all technical issues collaborated during the study. Students accessed this platform through an individual username and password in order to guarantee their anonymity.

Once data were obtained and stored, they were automatically transferred to an Excel file for subsequent processing. Process variables were based on frequency counts. Frequency of each sub-process or category was established by dividing the frequency of election of that category by the total number of elections done across categories.

These frequency counts were then transformed into percentages by multiplying the quotient by Finally, students' achievement in the mathematical tasks was established in terms of success 1 or failure 0 according to the answers given on paper. Given the main aims of this study, centered in the process, RT's as a meaure of effort were not taken into account for data analyses. Data analyses Ex - post - facto descriptive and comparative design was used in this study.

After describing the profile of process followed by the total group in each task, Multivariate Analysis of Covariance MANCOVA analyses with process variables 8 categories and 3 higher - level categories as dependent variables, and gender and level as covariates, were conducted in order to investigate differences between groups with different achievement.

Tasks were analysed separately in order to determine the importance of task difficulty as a factor explaining these differences. Data were analyzed with SPSS The additional category named "Other" was not taken into account for further analyses.

Student problem - solving process In order to demonstrate if a student's problem-solving process responds to SRL phases, Figure 1 shows the profile of the process followed by students in Tasks 1 and 2. This profile indicates similar processes for both tasks, characterized by a higher frequency of selected categories in planning and execution phases. The means Table II indicated a percentage of With respect to the revision phase, mean percentages of categories reported within this phase were It must be noted in this case the high means found in the planning phase even above those found in the execution phase.

This is because the planning phase consists of four sub-processes or categories, while the other phases comprise two. Tasks 1 and 2. With respect to execution phase, "mental calculation" was the category most frequently reported in this phase, with mean percentages of In relation to the revision phase, "reviewing" and "correcting mistakes" were two of the least frequently reported categories by students in both tasks 6.

Finally, standard deviations in Table II showed a high variability among the processes shown by students in both tasks, mainly in the categories less reported "recalling similar problems", "reviewing" and "correcting mistakes". Group - compositions revealed the presence of a high proportion of students solving the mathematical problems unsuccessfully.

Specifically, students As one of the aims of this study was to know whether there were differences between tasks with varying difficulty, separate analyses for each task were conducted. For the first task, means in Table III indicated a trend to plan more, and to execute and review less, in the Group 1 success. As happened with planning, this sub-process was more frequently reported by students who successfully solved the task. Task 1 With respect to the second task, the means in Table IV showed a different pattern of results, with students who successfully solved the problem reporting using less sub-processes related to planning, and more related to the execution and revision phases.

These differences were found in those categories or sub-processes within the planning phase: Means revealed that students who successfully solved the task Group 1 reported reading, recalling similar problems, and thinking about solutions less frequently than the other group.

As with the first task, successful students also reported using representation strategies i. In this context, the main aim of this study was to analyse the usefulness of a new assessment tool based on the Triple Task procedure and designed to assess the metacognitive and self - regulated processes shown by the fifth and sixth grade students during the performance of two mathematical problems of varying difficulty. Specifically, this study tried to answer these questions: Do students follow Self - Regulated Learning stages while they try to solve mathematical problems?

Global results indicated the presence of important differences among processes followed by students, as indicated by the high standard deviations. This variability was even higher in the categories or sub-processes less frequently reported by students in general: The pattern of results was similar in both tasks, and was characterized by a lack of evaluation strategies.

However, sub-processes related to Planning and Execution phases were the most frequently reported, respectively. However, despite the fact that these results could indicate that once students properly planned an activity, making mistakes became less likely and reviewing activities less necessary, students' achievements in both tasks revealed a high proportion of failure.

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This indicated that planning strategies were not effective enough. In fact, an analysis of the sub-processes involved in the planning phase revealed that thinking about solutions and reading were the most frequently reported sub-processes within planning, while the use of potentially more useful strategies such as information representation and organization were less frequent among students. This result could indicate a trend to use passive solving strategies or even comprehension difficulties.

Are there differences in the processes followed by students with different achievements in the tasks? Analyses revealed the existence of statistically significant differences between groups. These differences were located in the subprocess of drawing or summarizing in Problem 1, while significant differences were found in all the sub-process within the planning phase in Problem 2.

The existence of more significant differences in this second problem could be related to its characteristics i. Thus, this task may result more difficult, suggesting a more important role of planning strategies when problem difficulty and demands increase. Regarding the pattern of differences, students who successfully solved the tasks tended to draw and summarize more, but they recalled similar problems, read and thought about solutions proportionally less than those who failed to solve the tasks.

These results are consistent with the statement above about the effectiveness of planning strategies, and suggest the use of more active processes by students with high achievement.

In this sense, the strategy that showed to be effective in both tasks was drawing or summarizing i.

resolucion de problemas matematicos online dating

An example of graphical representation, made by a participant in this study, is shown in Figure 2. As Montague and othersp. In fact, Abdullah and others showed in their study that when the teaching approaches encourage students to apply thinking strategies through using visual representation, students are able to gain a better conceptual understanding and eventually improve their mathematics achievement.

They attributed this effect to a more active involvement of students in their learning process. However, representation is not only a matter of copying what one sees. As the example above shows, it involves a process of personal re-organization, inventing or adapting conventions of a representational system for the purpose at hand Stylianou, Are there differences between tasks with varying difficulty?

Although differences in the main phases of planning, execution and review were not statistically significant, analyses revealed the existence of significant differences in the sub-process involved in planning, separately.

resolucion de problemas matematicos online dating

In this way, differences in the metacognitive process showed by the groups with different achievement were stronger in Task 2, which implied more relationships to stablish and maybe more complex.

This would initially suggest a more important role of planning strategies when task difficulty and demands increase.

USANDO LAS TIC EN LA RESOLUCIÓN DE PROBLEMAS MATEMÁTICOS. by Amelinda Yas on Prezi

In fact, students in this study reported having planned. However, an in-depth analysis of the sub-process involved in planning revealed the presence of ineffective planning strategies implemented by the overall group, which was translated into a greater percentage of failure in both problems.

In this sense, another important finding of this study is that students had serious difficulties to evaluate their progress. They also showed a tendency to use familiar procedures, such as performing calculations, as a method to solve the problems.

resolucion de problemas matematicos online dating

Thus, students in this study did not self - regulate or implement effective metacognitions during problem solving. However, differences between groups with different achievement levels suggested that, despite the fact that students did not show a properly self - regulated process, a proportion of them were able to use more effective and active strategies while solving the problems, such as organizing or representing the information.

This is in fact an important determinining factor in successful mathematical problem solving. Finally, the use of effective planning strategies seemed to be most important when the task difficulty and demands are greater. These findings add evidence to the utility of process measures, specifically those based on directed and concurrent self - reporting, in the assessment of cognitive activities in this case mathematical problem - solving tasks.

The usefulness of the assessment tools presented in this studylies, however, in the systems of categories designed, which makes it possible to divide mathematical problem - solving tasks into sub-processes or isolated activities, and provides in-depth insights about a student's strengths or weaknesses, thereby helping to understand their success or failure from the point of view of SRL.

This is not only important for instruction, but specially for student learning. In this sense, as Ifenthaler pointed out, the key link between knowledge about and the regulation of one's own problem - solving activities may lie in reflective thinking.

Making students aware of their own learning processes may help them generate information about the efficiency of their problem-solving strategies and successfully implement that knowledge in the ongoing problem-solving process, thereby being able to control and regulate their cognition, effort and behavior.

It is necessary to acknowledge, however, the following limitations in the present study: The study conducted by Ahmed et al. Complementary use of both measures would provide a better understanding of self - regulatory mechanisms exhibited by the students, thus helping to design more adapted instructional strategies; finally, and given the characteristics of the sample students belonged to different schools in a specific area in Northern Spainextending the research to other areas would be advisable in order to better stablish the scope of the findings.

This is, however, the first approach to the study of the usefulness of the Triple Task technique in the assessment of the process involved in solving mathematical problems. Therefore, the results from the present study actually open the way for future research. In this sense, it would be interesting, for example, to conduct multi - level modeling that would take in to account school level effects.