scholarly journals THE TAXONOMY OF THE QUESTIONS IN THE ITALIAN NATIONAL ASSESSMENT OF KNOWLEDGE OF MATHEMATICS

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Daniel Doz
Keyword(s):  
Problem Solving ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
National Assessment ◽  
Language Of Instruction ◽  
Taxonomic Level ◽  
The Past ◽  
Closed Type ◽  
Level Problem ◽  
Official Data

In Italy, all grade 10 students are required to take the national assessment of knowledge of mathematics, which is prepared by the INVALSI Institute. No official data about any taxonomic level of the questions in these assessments has been published on the Institute’s website. In the present work, we analyzed seven INVALSI examinations for school with Slovene as language of instruction and we focused on the Gagne’s taxonomic level of each individual question in the assessments. The most frequent category in national assessments is “Routine procedural knowledge”, followed by “Basic and conceptual knowledge”. We found that, even though the interest in problem-solving activities has increased in the past years, the taxonomic level “Problem-solving knowledge” is the less frequent. Moreover, we wanted to analyze the distribution of the different taxonomic levels among the question typologies (open- and closed-type questions) and we found that questions from lower taxonomic levels are more likely to be closed-type, while “Problem-solving questions” are more likely to be open-type. Furthermore, we were interested in analyzing the distribution of taxonomic levels among the four topic dimensions “Geometry”, “Data and prevision”, “Numbers and quantities” and “Relations and functions”. We found that the taxonomic level “Problem-solving knowledge” are more present in the categories “Number and quantities” and “Relations and functions”.

Teaching Toward the Big Ideas of Algebra

2000 ◽  
Vol 6 (4) ◽  
pp. 226-231
Author(s):  
Sonia Woodbury
Keyword(s):  
Problem Solving ◽  
Conceptual Knowledge ◽  
Middle Grades ◽  
Procedural Knowledge ◽  
Conceptual Structure ◽  
Algebraic Manipulation ◽  
Relational Understanding ◽  
The Past ◽  
Starting Point ◽  
Big Ideas

IN WHAT WAYS DO WE WANT MIDDLE-GRADES STUDENTS TO UNDERSTAND ALGEBRA? Hiebert and Carpenter (1992) describe the need for students to gain both procedural knowledge and broadly connected conceptual knowledge to understand mathematics. A knowledge of rules and procedures provides students with tools for efficient problem solving. However, in learning the procedures of algebraic manipulation, for example, students often develop what Skemp (1978) calls an “instrumental understanding” of algebra. He explains, “It is what I have in the past described as ‘rules without reasons,’ without realizing that for many pupils… the possession of such a rule, and the ability to use it, was what they meant by ‘understanding’ ” (p. 9). Skemp contrasts instrumental understanding with “relational understanding,” which “consists of building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (p. 14).

The Writing Process: A Strategy for Problem Solvers

1990 ◽  
Vol 38 (3) ◽  
pp. 35-38
Author(s):  
Margaret I. Ford
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Writing Process ◽  
School Mathematics ◽  
Problem Solver ◽  
Educational Progress ◽  
National Assessment ◽  
The Past ◽  
Mathematics Educators ◽  
Problem Solvers

Over the past decade, mathematics educators have promoted problem solving as the goal of school mathematics. Yet in 1987, the National Assessment of Educational Progress revealed that our nation's schoolchildren are still falling short of our goals for their problem solving abilities. Many students dislike word problems in mathematics, and many teachers report feeling frustration and discouragement in helping their students learn how to solve such problems (Ford 1988). What can teachers do to improve students' attitude toward problem solving and to realize the goal of helping students become better problem solver?

One Point of View: Beyond the Textbook

1981 ◽  
Vol 28 (7) ◽  
pp. 2
Author(s):  
Carole E. Greenes
Keyword(s):  
Problem Solving ◽  
Point Of View ◽  
Educational Progress ◽  
National Assessment ◽  
The Past

For the past five years, we educators have been bombarded with data indicating that our students cannot solve problems. Results of the second evaluation of student abilities in mathematics by the National Assessment of Educational Progress not only demonstrated that students' problem-solving ability was poor, but also that this ability has declined in recent years. This is not surprising considering the emphasis placed on computation since the beginning of the “back-to-basics” movement more than seven years ago.

Mathematics Teachers' Conceptual Knowledge of Algebra: A Literature Review/ Pengetahuan Konseptual Algebra Guru Matematik: Satu Kajian Literatur

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Nor Adibah Abdullah
Keyword(s):  
Literature Review ◽  
Mathematics Teachers ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Secondary School Teachers ◽  
Past Research ◽  
Knowledge Level ◽  
School Teachers ◽  
The Past ◽  
Research Findings

Conceptual knowledge is one of the mathematical knowledge areas which should be mastered by mathematics teachers besides factual, procedural, and metacognitive knowledge. Teachers are prone to cast conceptual knowledge aside and prioritise procedural knowledge without understanding the concepts which influence the options of mathematical strategies and models in the context of problem solving. A literature review was conducted to discuss past research findings in identifying secondary school teachers' conceptual knowledge in the algebra topic. 68 past research articles were referred to and chosen based on the research purpose which was to investigate mathematics teachers' conceptual knowledge level and its implementation in several mathematical topics quantitatively and qualitatively in local and international contexts.  There have been a lot of researches conducted on teachers' conceptual knowledge in several mathematical topics, however there is still a lack of research in investigating teachers' conceptual knowledge on the algebra topic. Most of the past research findings showed that the teachers' conceptual knowledge level was at a low level in several mathematical  topics therefore a similar research is also needed in the algebra topic. This study can be extended to a more improved research in spite of the research sample, design or research methodology, instruments, and other factors. 

Truth Matters: Cognitive Integrity as an Intervention for Self-Deception

2017 ◽  
Author(s):  
Eugenia Isabel Gorlin ◽  
Michael W. Otto
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Autonomous Agents ◽  
Therapeutic Interventions ◽  
Empirical Validation ◽  
The Past ◽  
Adaptive Problem

To live well in the present, we take direction from the past. Yet, individuals may engage in a variety of behaviors that distort their past and current circumstances, reducing the likelihood of adaptive problem solving and decision making. In this article, we attend to self-deception as one such class of behaviors. Drawing upon research showing both the maladaptive consequences and self-perpetuating nature of self-deception, we propose that self-deception is an understudied risk and maintaining factor for psychopathology, and we introduce a “cognitive-integrity”-based approach that may hold promise for increasing the reach and effectiveness of our existing therapeutic interventions. Pending empirical validation of this theoretically-informed approach, we posit that patients may become more informed and autonomous agents in their own therapeutic growth by becoming more honest with themselves.

scholarly journals Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Jackson Pasini Mairing
Keyword(s):  
Problem Solving ◽  
Procedural Knowledge ◽  
Mental Image ◽  
Research Subjects ◽  
Maximum Score ◽  
Mathematical Problems ◽  
Problem Solving Strategies ◽  
Thinking Process ◽  
Problem Solvers ◽  
Holistic Rubric

Solving problem is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe the thinking process of naive problem solvers based on heuristic of Polya. The researcher gave two problems to students at grade XI from one of high schools in Palangka Raya, Indonesia. The research subjects were two students with problem solving scores of 0 or 1 for both problems (naive problem solvers). The score was determined by using a holistic rubric with maximum score of 4. Each subject was interviewed by the researcher separately based on the subject’s solution. The results showed that the naive problem solvers read the problems for several times in order to understand them. The naive problem solvers could determine the known and the unknown if they were written in the problems. However, they faced difficulties when the information in the problems should be processed in their mindsto construct a mental image. The naive problem solvers were also failed to make an appropriate plan because they did not have a problem solving schema. The schema was constructed by the understanding of the problems, conceptual and procedural knowledge of the relevant concepts, knowledge of problem solving strategies, and previous experiences in solving isomorphic problems.

scholarly journals The tip of the iceberg in organic chemistry classes: how do students deal with the invisible?

2015 ◽  
Vol 16 (1) ◽  
pp. 9-21 ◽  
Author(s):  
Nicole Graulich
Keyword(s):  
Organic Chemistry ◽  
Problem Solving ◽  
Cognitive Skills ◽  
Conceptual Knowledge ◽  
Chemistry Education ◽  
Scholarly Work ◽  
Related Research ◽  
Research Areas ◽  
Research Activities ◽  
Problem Solving Behavior

Organic chemistry education is one of the youngest research areas among all chemistry related research efforts, and its published scholarly work has become vibrant and diverse over the last 15 years. Research on problem-solving behavior, students' use of the arrow-pushing formalism, the investigation of students' conceptual knowledge and their cognitive skills have shaped our understanding of college students' understanding in organic chemistry classes. This review provides an overview of research efforts focusing on student's perspectives and summarizes the main results and pending questions that may guide subsequent research activities.

Republican conception of liberty in early republican Turkey and its contemporary implications

2015 ◽  
Vol 42 (4-5) ◽  
pp. 429-439
Author(s):  
Boğaç Erozan
Keyword(s):  
Problem Solving ◽  
Ample Evidence ◽  
Republican Period ◽  
Initial Failure ◽  
The Past ◽  
Political Problem ◽  
The Republic ◽  
Early Republican

Established in 1923, Turkey has been a republic without a dominant republican conception of liberty. A chance to install such a conception was missed in the early republican period and never recaptured. The republic was unable to get rid of vestiges of the authoritarian tradition of the past. Centuries-old authoritarian tradition persisted well into the recent and the contemporary periods. Presenting ample evidence, the article underlines the weight of history and the legacy of authoritarian mentality that promoted the use of authority, not liberty, in political problem-solving. The initial failure to abandon an authoritarian problem-solving approach proved fateful for the chances of the deepening of democracy in Turkey.

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