Learning progressions and the Australian curriculum mathematics: The case of statistics and probability

2021 ◽  
pp. 000494412110365
Author(s):  
Rosemary Callingham ◽  
Jane Watson ◽  
Greg Oates
Keyword(s):  
Problem Solving ◽  
Curriculum Development ◽  
Content Knowledge ◽  
Cognitive Processes ◽  
Statistical Reasoning ◽  
Learning Progressions ◽  
New Approach ◽  
Australian Curriculum ◽  
Statistics And Probability ◽  
Mathematics Curricula

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as ‘proficiencies’ that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies – reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability.

scholarly journals Remote Virtual Simulation for Incident Commanders—Cognitive Aspects

2021 ◽  
Vol 11 (14) ◽  
pp. 6434
Author(s):  
Cecilia Hammar Wijkmark ◽  
Maria Monika Metallinou ◽  
Ilona Heldal
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Cognitive Processes ◽  
Research Methodology ◽  
Current Knowledge ◽  
Learning Objectives ◽  
Virtual Simulation ◽  
Practical Training ◽  
Case Research ◽  
Action Case

Due to the COVID-19 restrictions, on-site Incident Commander (IC) practical training and examinations in Sweden were canceled as of March 2020. The graduation of one IC class was, however, conducted through Remote Virtual Simulation (RVS), the first such examination to our current knowledge. This paper presents the necessary enablers for setting up RVS and its influence on cognitive aspects of assessing practical competences. Data were gathered through observations, questionnaires, and interviews from students and instructors, using action-case research methodology. The results show the potential of RVS for supporting higher cognitive processes, such as recognition, comprehension, problem solving, decision making, and allowed students to demonstrate whether they had achieved the required learning objectives. Other reported benefits were the value of not gathering people (imposed by the pandemic), experiencing new, challenging incident scenarios, increased motivation for applying RVS based training both for students and instructors, and reduced traveling (corresponding to 15,400 km for a class). While further research is needed for defining how to integrate RVS in practical training and assessment for IC education and for increased generalizability, this research pinpoints current benefits and limitations, in relation to the cognitive aspects and in comparison, to previous examination formats.

scholarly journals Does Exposure to Multicultural Experience Enhance All Individuals’ Creative Problem-Solving Ability?

2017 ◽  
Vol 5 (2) ◽  
pp. 14 ◽  
Author(s):  
Mehrdad Fazeli Falavarjani ◽  
Forozan Irandust
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
Interactive Effect ◽  
Openness To Experience ◽  
Interactive Effects ◽  
Creative Problem Solving ◽  
Multicultural Experience ◽  
Diverse Community ◽  
Creative Problem ◽  
Cultural Cues

Today’s diverse community often includes culturally rich environments that contain cues pertaining to more than one culture. These cultural cues can shape cognitive processes, such as creativity. This study aims to investigate the interactive effects of Openness to Experience, Extroversion and Multicultural Experience (including the real and desired experiences) on creative problem-solving ability using the quantitative method on a diverse sample of international students (N= 102). The findings indicate that the interactive effect of extensive multicultural experience and Openness to Experience predict the creative solution. It means the multicultural experience is beneficial for individuals to foster creative ability when they are highly open to experience, whereas, among those who are not open, more extensive multicultural experience do not lead to enhancement of creating the correct solution. Furthermore, this interaction term was not pronounced among the extroverted individuals. Implications of these findings for promoting creativity in learning environments are discussed.

scholarly journals Fascinatin’ Rhythm – and Pauses in Translators’ Cognitive Processes

2018 ◽  
pp. 29
Author(s):  
Ricardo Muñoz Martín ◽  
Celia Martín de Leon
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
Sustained Attention ◽  
Initial Phase ◽  
Lower Threshold ◽  
Log Files ◽  
Information Searches ◽  
Log File

The Monitor Model fosters a view of translating where two mind modes stand out and alternate when trying to render originals word-by-word by default: shallow, uneventful processing vs problem solving. Research may have been biased towards problem solving, often operationalized with a pause of, or above, 3 seconds. This project analyzed 16 translation log files by four informants from four originals. A baseline minimal pause of 200 ms was instrumental to calculate two individual thresholds for each log file: (a) A low one – 1.5 times the median pause within words – and (b) a high one – 3 times the median pause between words. Pauses were then characterized as short (between 200 ms and the lower threshold), mid, and long (above the higher threshold, chunking the recorded activities in the translation task into task segments), and assumed to respond to different causes. Weak correlations between short, mid and long pauses were found, hinting at possible different cognitive processes. Inferred processes did not fall neatly into categories depending on the length of possibly associated pauses. Mid pauses occurred more often than long pauses between sentences and paragraphs, and they also more often flanked information searches and even problem-solving instances. Chains of proximal mid pauses marked cases of potential hesitations. Task segments tended to happen within 4–8 minute cycles, nested in a possible initial phase for contextualization, followed by long periods of sustained attention. We found no evidence for problem-solving thresholds, and no trace of behavior supporting the Monitor Model. 

scholarly journals STUDENTS’ COGNITIVE PROCESSES IN SOLVING PROBLEM RELATED TO THE CONCEPT OF AREA CONSERVATION

2019 ◽  
Vol 10 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Rooselyna Ekawati ◽  
Ahmad Wachidul Kohar ◽  
Elly Matul Imah ◽  
Siti Maghfirotun Amin ◽  
Shofan Fiangga
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
Cognitive Process ◽  
Low Achievers ◽  
High Achievers ◽  
Seventh Graders ◽  
Test Results ◽  
Area Formula ◽  
High Achiever ◽  
Cyclic Processes

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area conservation test. Results indicate that both samples performed more cyclic processes on formulating solution planning, regulating solution part and detecting and correcting error during the problem-solving. However, it was found that the high achiever student performed some processes than those of low achiever. Also, while the high achiever student did not predict any outcomes of his formulated strategies, the low achiever did not carry out the thought process after detecting errors of the initial solution gained. About the concept of area conservation, the finding also reveals that within the samples’ cognitive processes, the use of area formula come first before students decided to look for another strategy such as doing ‘cut-rotate-paste’ for the curved planes, which do not have any direct formula. The possible causes of the results were discussed to derive some recommendation for future studies.

scholarly journals Japanese and Swedish Mathematics Teacher Educators’ Pedagogical Content Knowledge – An Institutional Perspective

2019 ◽  
Vol 21 ◽  
Author(s):  
Yukiko Asami-Johansson ◽  
Iiris Attorps
Keyword(s):  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Institutional Perspective ◽  
Pedagogical Content ◽  
Mathematics Teacher Educators ◽  
Structured Problem Solving ◽  
Area Determination

The aim of this paper is to investigate which kind of conditions and constraints affect Japanese and Swedish teacher educators’ pedagogical content knowledge (PCK). We analyse the praxeologies of the lessons in which the educators teach area determination. Our study shows that the Japanese teacher educators’ PCK are more explicitly shared by the community of the teacher educators compared to the Swedish counterpart. Also, the detailed Japanese curriculum and the structured problem solving approach promote to illustrate how to construct rich mathematical and didactical organisations for prospective teachers.

Understanding Statistics Cognition

2017 ◽  
pp. 10-56
Keyword(s):  
Cognitive Processes ◽  
New Approach ◽  
Relationship Of ◽  
The Relationship

This chapter focuses on understanding the use of and relationship among the features of statistics cognition: literacy, reasoning, and thinking. We argue that research on statistics cognition is fragmented, which is problematic for understanding how these constructs can be unified to support education. We then review methods of quantifying cognitions, involving studies which have attempted to categorize and parse cognitive processes. This information is then used to synthesize a new approach to understanding statistics cognition, proposing a model which makes specific predictions about the relationship of these features. The model and definitions of cognitions presented in this chapter are used as a basis of discussion cognition throughout the remainder of the book.

Collaborative Solution Discovery: A Problem Solving Process

2019 ◽  
pp. 100-103
Author(s):  
Katharine Clemmer
Keyword(s):  
Problem Solving ◽  
Learning Environment ◽  
Real Time ◽  
School System ◽  
Mathematical Thinking ◽  
Self Regulation ◽  
Math Learning ◽  
New Approach ◽  
Problem Solving Process ◽  
The Way

Loyola Marymount University (LMU) has developed a new approach to problem solving, Collaborative Solution Discovery (CSD), to help practitioners in a school system leverage their individual passions in a way that grows students’ positive math identity through mathematical thinking, problem solving, and self-regulation. By focusing on how students and teachers interact with each other in real-time in an ideal classroom, practitioners take ownership of a process to guide their students in growing their positive math identity and thus taking ownership of their own math learning. Practitioners measure progress along the way through metrics that are created, defined, used, and continually refined by themselves to attain their ideal math learning environment. The entire CSD process results in a system that owns ist improvement efforts—improvement efforts that are flexible, adaptable, and sustainable.

Learning Progressions as Tools For Curriculum Development

2012 ◽  
pp. 359-403 ◽  
Author(s):  
Marianne Wiser ◽  
Carol L. Smith ◽  
Sue Doubler
Keyword(s):  
Curriculum Development ◽  
Learning Progressions
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