Generalization Strategies in Finding the <i>n</i>th Term Rule for Simple Quadratic Sequences

In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. Our aims are to identify their strategies and to explore whether and how format influences these strategies. Qualitative analysis of eye-tracking data offers several strategies: Sequence of Differences, Building a Relationship, Known Formula, Linear Recursive and Initial Conjecture. Sequence of Differences was the most common strategy, but Building a Relationship was more likely to lead to the right formula. Building from Square and Factor Search were the most successful methods of Building a Relationship. Findings about the influence of format on the range of strategies were inconclusive but analysis indicated sporadic evidence of possible influences

Algebraic generalization strategies of number patterns used by pre-service elementary mathematics teachers

AbstractThis study investigates algebraic generalization strategies of 147 pre-service elementary mathematics teachers. Pre-service teachers were given five open ended linear and non-linear (quadratic) pattern problems which require them to find the general term of number patterns. Pre-service teachers’ strategies to generalize and their use of mathematical models were analyzed. The analysis of data indicated that pre-service teachers described number pattern rules in relation to differences between terms and used visual models without a purpose

Comparison of religious slaughter of sheep with methods that include pre-slaughter stunning, and the lack of differences in exsanguination, packed cell volume and meat quality parameters

UK legislation requiring pre-slaughter stunning has certain exemptions for religious slaughter. Supporters of both Muslim (Halal) and Jewish (Shechito) slaughter methods claim that the efficiency of the bleed out is adversely affected by stunning. In this study, electrical stunning followed by neck cutting, and captive bolt stunning followed by neck cutting, were compared with the Muslim slaughter method (neck cutting without stunning) in sheep. Total blood loss and percentage blood loss, expressed as a percentage of live weight were calculated and compared between groups. In addition, the time taken to reach 25%, 50%, 75% and 90% of total blood loss was calculated and compared. There was no apparent difference in the packed cell volume levels between groups. Slaughter method did, however, affect meat pH and colour. The results show that the bleed out after neck cutting is not adversely affected by electrical or captive bolt stunning, nor is an improved bleed out achieved by neck cutting without stunning