Jan Mokros

Bio: Jan Mokros is an academic researcher. The author has contributed to research in topics: Class (set theory) & Data literacy. The author has an hindex of 2, co-authored 3 publications receiving 266 citations.

Children's Concepts of Average and Representativeness.

Abstract: Whenever the need arises to describe a set of data in a succinct way, the issue of mathematical representativeness arises. The goal of this research is to understand the characteristics of fourth through eighth graders' constructions of "average" as a representative number summarizing a data set. Twenty-one students were interviewed, using a series of open-ended problems that called on children to construct their own notion of representativeness. Five basic constructions of representativeness are identified and analyzed. These approaches illustrate the ways in which students are (or are not) developing useful, general definitions for the statistical concept of average. One objective of statistics is to reduce large, unmanageable, and disordered collections of information to summary representations. The need to summarize data is present even among young children. For example, in the surveys conducted by primary-grade students, we see movement from focusing on individual pieces of data ("I have one brother") to highlighting and summarizing the data in some manageable form ("Most of the class members have only one brother or sister"). As soon as there is the need to describe a set of data in a more succinct way, the notion of representativeness arises: What is typical of these data? How can we capture their range and distribution?

Zoos, aquariums, and expanding students' data literacy

Abstract: Field trips provide compelling venues for teaching students to work with observational data and make important connections between mathematics and science.

Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction.

Abstract: Activities that promote student invention can appear inefficient, because students do not generate canonical solutions, and therefore the students may perform badly on standard assessments. Two studies on teaching descriptive statistics to 9th-grade students examined whether invention activities may prepare students to learn. Study 1 found that invention activities, when coupled with subsequent learning resources like lectures, led to strong gains in procedural skills, insight into formulas, and abilities to evaluate data from an argument. Additionally, an embedded assessment experiment crossed the factors of instructional method by type of transfer test, with 1 test including resources for learning and 1 not. A "tell-and-practice" instructional condition led to the same transfer results as an invention condition when there was no learning resource, but the invention condition did better than the tell-and-practice condition when there was a learning resource. This demonstrates the value of invention activ...

The challenge of developing statistical literacy, reasoning and thinking

Abstract: Statistical Literacy, Reasoning, and Thinking: Goals, Definitions, and Challenges.- Towards an Understanding of Statistical Thinking.- Statistical Literacy.- A Comparison of Mathematical and Statistical Reasoning.- Models of Development in Statistical Reasoning.- Reasoning about Data Analysis.- Learning to Reason About Distribution.- Conceptualizing an Average as a Stable Feature of a Noisy Process.- Reasoning About Variation.- Reasoning about Covariation.- Students' Reasoning about the Normal Distribution.- Developing Reasoning about Samples.- Reasoning about Sampling Distribitions.- Primary Teachers' Statistical Reasoning about Data.- Secondary Teachers' Statistical Reasoning in Comparing Two Groups.- Principles of Instructional Design for Supporting the Development of Students' Statistical Reasoning.- Research on Statistical Literacy, Reasoning, and Thinking: Issues, Challenges, and Implications.

How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics

Abstract: Summary This paper provides an overview of current research on teaching and learning statistics, summarizing studies that have been conducted by researchers from different disciplines and focused on students at all levels. The review is organized by general research questions addressed, and suggests what can be learned from the results of each of these questions. The implications of the research are described in terms of eight principles for learning statistics from Garfield (1995) which are revisited in the light of results from current studies.

Using Questioning to Guide Student Thinking

Abstract: This case study analyzes ways in which an experienced physics teacher uses questioning to guide student thinking during a benchmark discussion about measurement. Interactional issues involve ways of speaking: Why the teacher decided to ask what he did, when he did, of whom, in what way, and for what purpose. Conceptual issues involves ways of thinking: How students seemed to understand measurement concepts such as calculating an average value. We define a particular kind of question, a reflective toss, that the teacher uses to try to give students responsibility for thinking. A reflective toss sequence typically consists of a student statement, teacher question, and additional student statements. This unit of analysis directs attention to ways in which a teacher question influences student thinking. We analyze reflective tosses in terms of the immediate action plans they instantiated, the emergent goals they served, anal underlying beliefs they embodied during an episode that involved the public refinemen...

Beyond Being Told Not to Tell

Abstract: For the past several years, we have been developing and studying teaching practices through our own efforts to teach school mathematics. Ball's work has been at the elementary level, in third grade, and Chazan's at the secondary level, grade ten and above, in Algebra I. In our teaching, we have been attempting, among other things, to create opportunities for classroom discussions of the kinds envisioned in the US National Council for Teachers of Mathematics Standards (NCTM, 1989, 1991). At the same time, we have been exploring the complexities of such practice. By using our teaching as a site for research into, and as a source for formulating a critique of, what it takes to teach in the ways reformers promote, we have access to a particular 'insider' sense of the teacher's purposes and reasoning, beyond that which a researcher might have. [1] This article originated with frustration at current math education discourse about the teacher's role in discussion-