Abstracts for some of the talks at the AMBLE symposium 2016.
Mathematics as a tool for understanding the world
Professor, Department of Education, University of Oxford
Cultural tools allow humans to overcome their biological limitations. Our eyes cannot see blood cells: we use microscopes and see them. We cannot recall millions of words in a fixed order: number systems allow us to generate millions of counting words in a fixed order. Number systems allow us to represent quantities when they are not in view, to make comparisons between quantities which our perceptual systems would be unable to make, and to reason about quantities by operating on the numbers that represent them. In this talk, I invite you to think about how children learn about numbers, quantities, and relations. Children are able to use quantitative representations and operate on them before they can calculate using numbers. When mathematical knowledge is developed mostly outside school, children’s quantitative reasoning can be ahead of their number knowledge. But if they learn to include conventional number systems in their reasoning, they can use mathematics to understand the world.
Impressions from longitudinal studies to interventions: number-specific and domain-general cognitions
Executive vice director, clinical neuropsychologist, Niilo Mäki Institute, Jyväskylä, Finland
Building an understanding how the numerical cognition develops is needed for building effective intervention programs on mathematical skills. In this presentation I will highlight three details, which we have studied together with our collaborators from different research institutions. I will start from our results from longitudinal follow-up and brain imaging studies to explain the expected relationships between these cognitions and mathematical skills. Those will be followed by results from studies on specifically designed intervention programs trying to catch some of the vital elements of those phenomena. The first detail is the child’s own spontaneous attention to amounts in his/her environment, the second is the approximate number system and number comparison behaviour, and the last is the visuo-spatial skills and visual working memory. There is a cumulating amount of studies showing that all these three different types of cognitions contribute strongly to the development of mathematical skills. I will try to connect these to intervention studies we have conducted: On sponaneus focusing together with colleagues from the University of Turku, number comparison together with INSERM from Paris and visuo-spatial skills with the Karolinska Institutet in Sweden. The intervention studies reveal new details about the relationships between these specific cognitions and learning basic numerical skills. These new details are a good starting point for further studies and understanding the developing mathematical brain.
Words and ideas, facts and knowledge: Promoting reading success
Professor, Harvard Graduate School of Education, Camebridge
Evidence is accumulating about the challenges good word readers often face in comprehending the texts they face after the first few years of school. We have tested the hypothesis that two capacities rarely addressed in traditional instruction — perspective-taking and academic language — are necessary for later reading comprehension. In addition, we know that world knowledge (often operationalized as vocabulary) is a strong predictor of comprehension success. I will describe approaches to ensuring that all students — in particular those most at risk because of social class or language minority status — have opportunities to build world knowledge and to develop academic language and perspective-taking skills, starting in preschool and continuing through the elementary years.
Inferencing: vocabulary matters!
Professor, Psychology and Language Sciences, University College London
Inferencing is a skill that requires individuals to go beyond what is explicitly stated and construct meaning by integrating prior knowledge with the surround linguistic context. Inferencing is a crucial skill that underpins comprehension of oral and written narratives. It is also a skill that many children with language and communication disorders find particularly challenging. The source of inferencing deficit in different clinical conditions is frequently debated; for instance it has been argued that inferencing deficits experienced by children with autism spectrum disorders stem from a core deficit in integrating information within context. In this talk, I will present evidence from two studies: first, a population study of 7-8 year old children with ‘specific’ language impairments, and second, a study of children with autism spectrum disorder with and without additional language impairment. Our findings demonstrate that vocabulary knowledge is essential for inferencing success and predicts variance in inferencing and narrative/text comprehension across clinical boundaries. Thus, interventions that improve breadth and depth of vocabulary knowledge could have positive downstream effects on the inferencing, and thus comprehension, skills of these children.
Why do so Many Children Struggle to Learn Fractions and How Can we Help Them?
Nancy C. Jordan
Professor, The Center for Improving Learning of Fractions, School of Education, University of Delaware
Fractions are foundational for learning algebra, thus representing a crucial component of STEM (science, technology, engineering and mathematics) education. Facility with fractions also affects daily life functioning in areas such as managing personal finances and making healthcare decisions. This presentation will synthesize findings to date from the Center for Improving Learning of Fractions. We followed a large cohort of children (N = 536) over four grades in elementary and middle school. Many students made minimal growth in fraction knowledge and some showed only a basic grasp of the meaning of a fraction, even after several years of instruction. Although a range of general cognitive and number specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a key marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to numerical magnitude representations that are further complicated by the introduction of fractions into the curriculum. The results of instructional interventions designed to address core fraction difficulties will be discussed.