Fast and frugal framing effects?

Three experiments examine whether simple pair-wise comparison judgments, involving the “recognition heuristic” (Goldstein & Gigerenzer, 2002), are sensitive to implicit cues to the nature of the comparison required. Experiments 1 & 2 show that participants frequently choose the recognized option of a pair if asked to make “larger” judgments but are significantly less likely to choose the unrecognized option when asked to make “smaller” judgments. Experiment 3 demonstrates that, overall, participants consider recognition to be a more reliable guide to judgments of a magnitude criterion than lack of recognition and that this intuition drives the framing effect. These results support the idea that, when making pair-wise comparison judgments, inferring that the recognized item is large is simpler than inferring that the unrecognized item is small.

Thinking skills in the early years: a literature review

Since 1999, thinking skills have been included in the National Curriculum alongside ‘key skills’ such as those to do with communication and information and communications technology (ICT). Thinking skills are expected to be developed at all key stages and centre on: information-processing skills, reasoning skills, enquiry skills, creative thinking skills and evaluation skills. This literature review consisted of three phases based on the following research questions: 1. What pedagogical approaches to developing generic thinking skills currently exist for children between the ages of three and seven? 2. What are the generic thinking skills that children are able to demonstrate at this age? 3. What is the relationship between these thinking capabilities and those that the pedagogical approaches aim to develop? The review covered post-2000 literature in the area of thinking skills in the early years. It provides an update of the evidence base upon which thinking skills approaches have been established, suggests areas where more evidence is needed and makes some practical recommendations for researchers, policy makers and practitioners.

The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘a’ means ‘apple’”) is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, “3a + 2a = 5a” to year 7 pupils. Results included the notion that the ‘algebra as object’ analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not ‘supposed’ to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an‘algebra as object’ approach. Year 7 pupils did not explicitly refer to ‘algebra as object’, although some of their responses could be so interpreted. In the main, year 10 pupils used ‘algebra as object’ to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of ‘algebra as object’ in pupils’ thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.

Everything and nothing project

An EPRSC ‘Partnerships for Public Engagement’ scheme 2010. FEC 122,545.56/UoR 10K everything and nothing is a performance and workshop which engages the public creatively with mathematical concepts: the Poincare conjecture, the shape of the universe, topology, and the nature of infinity are explored through an original, thought provoking piece of music theatre. Jorge Luis Borges' short story 'The Library of Babel' and the aviator Amelia Earhart’s attempt to circumnavigate the globe combine to communicate to audience key mathematical concepts of Poincare’s conjecture. The project builds on a 2008 EPSRC early development project (EP/G001650/1) and is led by an interdisciplinary team the19thstep consisting of composer Dorothy Ker, sculptor Kate Allen and mathematician Marcus du Sautoy. everything and nothing has been devised by Dorothy Ker and Kate Allen, is performed by percussionist Chris Brannick, mezzo soprano Lucy Stevens and sound designer Kelcey Swain. The UK tour targets arts-going audiences, from the Green Man Festival to the British Science Festival. Each performance is accompanied with a workshop led by Topologist Katie Steckles. Alongside the performances and workshops is a website, http://www.everythingandnothingproject.com/ The Public engagement evaluation and monitoring for the project are carried out by evaluator Bea Jefferson. The project is significant in its timely relation to contemporary mathematics and arts-science themes delivering an extensive programme of public engagement.

Vocabulary is important for some, but not all reading skills

Although there is evidence for a close link between the development of oral vocabulary and reading comprehension, less clear is whether oral vocabulary skills relate to the development of word-level reading skills. This study investigated vocabulary and literacy in 81 children aged 8 to 10 years. In regression analyses, vocabulary accounted for unique variance in exception word reading and reading comprehension, but not text reading accuracy, decoding, or regular word reading. Consistent with these data, children with poor reading comprehension exhibited oral vocabulary weaknesses and read fewer exception words correctly. These findings demonstrate that oral vocabulary is associated with some, but not all, reading skills. Results are discussed in terms of current models of reading development.

Investigating orthographic and semantic aspects of word learning in poor comprehenders

This study compared orthographic and semantic aspects of word learning in children who differed in reading comprehension skill. Poor comprehenders and controls matched for age (9-10 years), nonverbal ability and decoding skill were trained to pronounce 20 visually presented nonwords, 10 in a consistent way and 10 in an inconsistent way. They then had an opportunity to infer the meanings of the new words from story context. Orthographic learning was measured in three ways: the number of trials taken to learn to pronounce nonwords correctly, orthographic choice and spelling. Across all measures, consistent items were easier than inconsistent items and poor comprehenders did not differ from control children. Semantic learning was assessed on three occasions, using a nonword-picture matching task. While poor comprehenders showed equivalent semantic learning to controls immediately after exposure to nonword meaning, this knowledge was not well retained over time. Results are discussed in terms of the language and reading skills of poor comprehenders and in relation to current models of reading development.

Orthographic facilitation in oral vocabulary acquisition

An experiment investigated whether exposure to orthography facilitates oral vocabulary learning. A total of 58 typically developing children aged 8-9 years were taught 12 nonwords. Children were trained to associate novel phonological forms with pictures of novel objects. Pictures were used as referents to represent novel word meanings. For half of the nonwords children were additionally exposed to orthography, although they were not alerted to its presence, nor were they instructed to use it. After this training phase a nonword-picture matching posttest was used to assess learning of nonword meaning, and a spelling posttest was used to assess learning of nonword orthography. Children showed robust learning for novel spelling patterns after incidental exposure to orthography. Further, we observed stronger learning for nonword-referent pairings trained with orthography. The degree of orthographic facilitation observed in posttests was related to children's reading levels, with more advanced readers showing more benefit from the presence of orthography.