The study investigated critical thinking among online mathematics teachers through analyzing discussions in an online course. It found evidence that assignments combining readings with classroom applications, open-ended mathematical problems with decision-making and applications, and lesson planning with instructor feedback elicited higher-level thinking. Assignments varied in structure and requirements within task types like readings, problems and realistic learning. The nature of tasks impacted cognitive presence, with certain problem-solving and applied assignments correlating with more integration and resolution of ideas.
15. Overall Category Counts for Postings Category Count % of All Messages % of PIM Messages % of PIM RP Excluded Triggering Event 6 .61 .73 1.17 Exploration 631 64.65 76.95 63.23 Integration 155 15.88 18.90 30.16 Resolution 28 2.87 3.41 5.45 Comments 88 9.02 NA NA Teacher Presence 68 6.97 NA NA
16. Number of postings per student per phase of the Practical Inquiry Model with required postings removed.
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19. Assignments Categorized by Task Type Task Type Assignments Description Readings 1,4,8 3 10,12 19 ERMO Biography Readings/applications to classroom Readings from text/online source Problems 2,6 9,13,14 7,17 11,15 Historical math problem – higher cognitive demand Historical math problem –lower cognitive demand Problem exploration based on Web applets Analyze a given proof Realistic 16,18 5 13 Lesson plan Discussion of classroom uses for math history Fibonacci problem given to students’ students
24. Research Question 1: Do the discussions generated in MATH 500 demonstrate evidence of higher level thinking in terms of cognitive presence?
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26. Research Question 2: Is there evidence of a relationship between the tasks that are implemented in MATH 500 and the levels of cognitive presence observed in the corresponding discussions?
27. Task Type Assignments Description Readings 1,4,8 3 10,12 19 ERMO Biography Readings/applications to classroom Readings from text/online source Problems 2,6 9,13,14 7,17 11,15 Historical math problem – higher cognitive demand Historical math problem –lower cognitive demand Problem exploration based on Web applets Analyze a given proof Realistic 16,18 5 13 Lesson plan Discussion of classroom uses for math history Fibonacci problem given to students’ students
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31. Research Question 3: What is the nature of the tasks that are implemented in MATH 500?
A combination of socio-culturalism, based on the ideas of Vygotsky, and the Community of Inquiry model, developed by Garrison, Anderson, & Archer (2001), form the theoretical basis for this study
Social Presence : the ability of learners to project themselves socially and effectively into a community of inquiry Social presence is a necessary element for creating a community of inquiry and encouraging deep approaches to learning, but is also insufficient (Garrison & Cleveland-Innes, 2005) Teaching Presence : the design, facilitation, and direction of cognitive and social processes Teaching presence that is student-centered is believed to be the link in transitioning students from purely social presence to cognitive presence (Garrison & Cleveland-Innes, 2005) Cognitive Presence : the extent to which participants are able to construct meaning through sustained communication “ Cognitive presence reflects higher-order knowledge acquisition and application and is most associated with the literature and research related to critical thinking” (Garrison, Anderson, & Archer, 2001) Cognitive presence focuses on the process of critical thinking, not the product that results
Triggering event: Teacher typically provides task but any group member can add to the discourse Exploration: Search for information, knowledge, and alternatives that might help to make sense of the situation or problem Integration: Integrating the information and knowledge from the exploratory phase into a coherent idea or concept Resolution: Consensus building within the community occurs and newly created knowledge is applied, tested, and defended.
Researcher-developed questionnaire -Age, gender, location, educational background, teaching background, online and MMTE experience -Used to compare demographics to individual cognitive presence Course instructor interview -Instructor background, MMTE program description, online learning beliefs, preferred online tasks -Used to build an accurate description of his background and the MMTE program and get his views on aspects of teaching and learning online -Used to create the task types Content Analysis - Garrisons coding protocol modified - All messages in the course were gone through - training with Art, email with Garrison
Used to triangulate content analysis results and to assess the nature of teaching and social presence elements
Based on cognitive presence indicators; used to triangulate cognitive presence coding results
Data was looked at as overall messages… The highest percentage of postings was coded as EX, next highest IN Explain last two columns
Data was looked at data by student ….
The ability of teachers to engage in knowledge construction with their peers might be directly related to the content knowledge they possess and the mathematics they teach on a daily basis.
Moving on to looking at the data by task type…
Example of how each type was looked at …
Things matched up!!!
Data by assignment… Hmmmm 2 & 6 stick out? Go back 3 slides!
Cognitive presence in terms of higher order thinking existed somewhere within each task type, but was not consistently represented across all assignments within each task type. Therefore, valid conclusions could not be made about the relationships between cognitive presence and task type. In an effort to make finer distinctions that might lead to reasonable conclusions about the data, the task types were further sub-grouped according to similarities the assignments shared.
Teaching presence of instructor may have hindered discussion in 18 but helped in 16
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