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Comprehending the Menger Sponge
Title
Comprehending the Menger Sponge
Creator
Alcheikh, Bassil, Leslie, Barett A., Pichardo, Brian
Date
2012-01-31, 2012-01-31
Description
This poster, created by undergraduate students at the Illinois Institute of Technology (IIT), details Karl Menger's 1926-discovered fractal...
Show moreThis poster, created by undergraduate students at the Illinois Institute of Technology (IIT), details Karl Menger's 1926-discovered fractal curve currently known as the Menger sponge. Menger is a former IIT faculty member.
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SIMILARITIES AND DIFFERENCES BETWEEN ACTUAL SCIENCE INSTRUCTION ENACTED IN THE HIGH SCHOOL CLASSROOM AND COLLEGE SCIENCE TEACHERS’ PERCEPTIONS OF STUDENTS’ KNOWLEDGE AND ABILITIES NECESSARY FOR ACADEMIC SUCCESS
Title
SIMILARITIES AND DIFFERENCES BETWEEN ACTUAL SCIENCE INSTRUCTION ENACTED IN THE HIGH SCHOOL CLASSROOM AND COLLEGE SCIENCE TEACHERS’ PERCEPTIONS OF STUDENTS’ KNOWLEDGE AND ABILITIES NECESSARY FOR ACADEMIC SUCCESS
Creator
Kedvesh, James
Date
2019
Description
The enacted curriculum and classroom artifacts of a full unit of instruction from three subject areas (biology, chemistry, and physics) at two...
Show moreThe enacted curriculum and classroom artifacts of a full unit of instruction from three subject areas (biology, chemistry, and physics) at two levels of instruction (regular and advanced) were analyzed for the presence and degree of mathematics and critical thinking. These characteristics were selected from a review of the literature on college science faculty’s views of best student preparation. Classes were grouped and compared by subject area and by level of science class. Varying degrees of critical thinking and mathematics were found to be present in the six observed classes, but both characteristics were found in all of the observed units of instruction. Comparisons of the statistical and practical differences found the greatest differences when comparing mathematics by subject area. These differences were not due to within subject area differences. Comparisons found the greatest similarities when comparing critical thinking by level of instruction. It was found that classroom pedagogy was a more important factor than subject area or level of instruction in determining the degree of alignment of classroom instruction with respect to the presence and inclusion of mathematics and critical thinking. Overall, there was a common lack of explicit instruction in both mathematics and critical thinking among all observed units of instruction. These findings support the need for more explicit mathematics and critical thinking instruction within science classes. Also, it is recommended that pre-service and practicing science teachers are prepared with the knowledge and methods of best mathematics instruction to better incorporate these strategies within and alongside their science instruction.
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WHAT IMPACT DO NUMBER TALKS HAVE ON ELEMENTARY CLASSROOM MATHEMATICAL DISCOURSE AND STUDENT AND TEACHER ATTITUDES TOWARD MATHEMATICS?
Title
WHAT IMPACT DO NUMBER TALKS HAVE ON ELEMENTARY CLASSROOM MATHEMATICAL DISCOURSE AND STUDENT AND TEACHER ATTITUDES TOWARD MATHEMATICS?
Creator
Sleezer, Meghan V
Date
2021
Description
Number Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community...
Show moreNumber Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community over the past decade with the publication of the book series Number Talks (Parrish, 2010, 2014), and especially since the publication of Making Number Talks Matter (Humphreys & Parker, 2015). All in all, the authors contend Number Talks can bring joy into the classroom (Humphreys and Parker, 2015, p. 6), improving student attitudes about mathematics and ultimately allowing for a more productive disposition. The characteristic that separates Number Talks from other pedagogical tools is the disconnectedness from the rest of the lesson: Number Talks need not build up to or build upon the day’s objective. Thus, what the authors argue is that the activity of Number Talks itself – albeit disconnected from the day’s objective – improves all of the aforementioned skills, regardless of what occurs during the remainder of each class session.Eight teachers from five different Chicago-area private grade schools implemented Number Talks in their 3rd-5th grade classrooms for four to six weeks in the early part of the year 2020. Student attitudes toward mathematics and toward mathematical discourse were assessed by way of survey and classroom observation before and after implementation. Classroom interactions and levels of mathematical discourse during the normal class time (outside of the Number Talk session) were assessed before and during implementation. No significant changes (positive or negative) relating to any measure were found. Teachers noticed that students who enjoyed math before the implementation also enjoyed Number Talks, while students who struggled with math were mostly disenchanted with Number Talks. Future research includes exploring whether tailoring Number Talks to relate to the upcoming lesson improves the positive effects advertised by the authors. Teacher professional development related to ambitious teaching practices (NCTM, 2017) and growth mindset (Boaler, 2016b) may complement the use of Number Talks to result in improved attitudes and discourse.
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Case Study: A Comparison of Pedagogical Content Knowledge Between Coaches and Coaches/Mentees
Title
Case Study: A Comparison of Pedagogical Content Knowledge Between Coaches and Coaches/Mentees
Creator
Barone, Ana MargaritaSalinas
Date
2024
Description
This multiple case study dissertation aimed to examine one of the domains of pedagogical content knowledge, knowledge of content and students,...
Show moreThis multiple case study dissertation aimed to examine one of the domains of pedagogical content knowledge, knowledge of content and students, between different types of elementary coaches and between coach and their respective collaborating teachers. It also investigated the impact a coaches’ background experiences have on the dynamic between coaches and teachers and the perceptions' teacher have on the effectiveness of coaching. The theoretical framework used in this qualitative study was Ball, Thames, and Phelps’ (2008) definition of PCK. Data was collected from six coaches–four instructional coaches and two math coaches–and eleven k-5th grade teachers. Data collection involved a survey, LMT assessment, and semi-structured interviews, and a thematic analysis method was conducted. The findings from the cross-case analysis resulted in ten themes, with the majority having multiple categories. One finding to one of the research questions was that there were no differences in knowledge of content and students between mathematics coaches and general instructional coaches, but other areas to further investigate emerged. Another finding was that coaches were either within the same capacity as their respective teachers or had extra knowledge of content and students. Although the majority of the coaches’ knowledge of content and students was at a higher level according to their LMT score, it does not necessarily mean that coaches are working with teachers in improving knowledge of content and students. In addition, more research is recommended in creating a pedagogical content knowledge instrument that is specific for coaches.
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