Constructing sample space with combinatorial reasoning: a mixed methods study

Recent curricular developments suggest that students at all levels need to be statistically literate and able to efficiently and accurately make probabilistic decisions. Furthermore, statistical literacy is a requirement to being a well-informed citizen of society. Research also recognizes that the ability to reason probabilistically is supported and enabled by other forms of mathematical reasoning and concepts. One of these supporting concepts is sample space, the enumeration of all outcomes of a probability experiment. As a concept, sample space supports the construction of probability distributions, which in turn enables statistical inference, a form of probabilistic reasoning. This mixed methods study investigated how undergraduate pre-service elementary teachers construct and generalize their understanding about sample space. One hundred fifty students participated in a series of three tasks designed to investigate the ways in which they enumerate sample space and the associations between their enumeration strategies and their generalization rules. A subset of eight participants engaged in follow- up interviews designed to explore their understandings of sample space enumeration and generalization. Findings from the study suggest that there was growth across tasks in the sophistication of the enumeration strategies used and that participants attempted to find explicit and formalized generalizations. However, in spite of this growth in the sophistication of enumeration, there was little association between the enumeration strategies participants used and the generalizations that they constructed. Students compartmentalized their understanding of generalization rules, often looking for a numeric formula that had little do to with their enumerated solutions

Traveling Representations in a Fifth Grade Classroom: An Exploration of Algebraic Reasoning

In this three-day teaching experiment along with follow up interviews, algebraic concepts related to pattern-finding tasks were examined with 25 fifth grade students. The specific focus centered on representations from a realistic mathematics education perspective, meaning a model “of” a situation toward a model “for” a situation. Within this context, certain situational models were found that seemed to travel and permeate throughout the entire class. Students were able to generalize and justify based on the models developed during whole class discussions. Several weeks after the teaching experiment, follow up interviews indicated that the representations generated were still prevalent in students’ descriptions of the activities. Findings, analysis of findings, and implications of the study will be discussed

Christmas and Me

Column contains Christmas message from Mac McGalliard and what the season means to him. Newspaper article, original, 2 copie

Rating By Citizens

Column concerns poll being taken by the Ardmore Jaycees questioning the public on their opinion of the city of Ardmore. Some of the questions are answered by McGalliard in the column. Newspaper article, origina

Ardmore Children's Shelter

Daily Ardmoreite, June 21, 1970, by Mac McGalliard. Story of opening of the shelter, brought about by the work of the Lion's Club, and other civic organizations

Budget-$1.98

Column includes: Comments on $99.7 billion budget submitted by Pres. Lyndon Johnson to Congress. Story of Clinton D. Arnot, General Dynamics official, married to Durant native. General Dynamics local at Ardmore Airpark is thriving. Successful photographers John Williams and Ivan Lawson, both former Daily Ardmoreite employees, are now independent businessmen

Chickasaw Festival Hot Assignment

Column concerns report of the first annual Chickasaw Festival held at Tishomingo. Dignitaries attending and view of the festival is included in the report. Newspaper article, origina

Chickasaws Hold Meeting

Daily Ardmoreite, Oct. 17, 1966, by Mac McGalliard. Story of the annual tribal meeting on the Kullihoma Reservation, north of Wapanucka, Oklahoma. Notes taken by Mac McGalliard and ribbons presented to attendees are included with the article

Old Oil Well Producing Again

Report that the Healdton discovery well, brought in on Aug. 4, 1913, was producing oil again for the Shell Oil Co. Water-flooding in the area had caused the well to produce up to 50 barrels a day at a time of the story. newspaper articl

Sales Tax and Streets

Column includes report of improvements to Ardmore streets due to the added revenue from the additional one-cent sales tax and visit to the sanitation department. Newspaper article, origina