For many students, algebraic formulas are abracadabra: they lack symbol sense. Symbol sense includes identifying the structure of algebraic formulas, giving meaning to them, and reasoning with and... Show moreFor many students, algebraic formulas are abracadabra: they lack symbol sense. Symbol sense includes identifying the structure of algebraic formulas, giving meaning to them, and reasoning with and about formulas. Besides basic skills, symbol sense is needed to solve algebraic problems and it is not known how to teach symbol sense systematically.In this research we have studied how teaching graphing formulas by hand (i.e. sketching a graph of a formula) could promote grade 11- and 12-students’ symbol sense. Our GQR-design (Graphing formulas through recognition and qualitative reasoning) is based on expert research and pays explicit attention to recognition of basic function families and features, and to qualitative reasoning, that focuses on the global shape of a graph, with global descriptions and ignoring what is not relevant. These aspects get little attention in regular education, that often focuses on algebraic manipulation.We found that students improved their insight into formulas and found a positive correlation between students’ abilities to graph formulas and their abilities to solve non-routine algebra problems with symbol sense. The students were able to use essential aspects of symbol sense, learned in the context of graphing formulas, such as taking a global view for recognition, qualitative reasoning, and questioning a formula, when solving algebra problems.In the future, when technology will take over the manipulation of algebraic formulas, symbol sense will become even more important. Graphing formulas could promote students’ symbol sense in upper secondary school, and therefore deserves a prominent place in mathematics curriculum. Show less
The term “cardiometabolic disease” describes a cluster of sub-clinical disorders that are shared by cardiovascular diseases and type 2 diabetes, including dyslipidaemia, and glucose intolerance. In... Show moreThe term “cardiometabolic disease” describes a cluster of sub-clinical disorders that are shared by cardiovascular diseases and type 2 diabetes, including dyslipidaemia, and glucose intolerance. In clinical settings, fasting measurement is still the gold standard for the diagnosis of hyperglycemia and dyslipidaemia. However, due to irregular meal intake, we spend the majority of our waking hours in a non-fasting state. The non-fasting state is a dynamic condition that is affected by many factors, including diet, lifestyle, physiological factors, pathological conditions, and genetics. Thus far, the genes and genetic loci that affect postprandial glucose and lipid metabolism have not been fully understood. By using the data from the Netherlands Epidemiology of Obesity study, we found 1) postprandial measures after a liquid mixed meal were as robust as fasting measures by repeated measures; 2) to stratify pre-diabetic individuals into high- and low-risk of developing to type 2 diabetes, the model performance by using postprandial metabolites was similar to the model performance using fasting metabolites; 3) the genetics of fasting and postprandial metabolite levels are highly overlapped. All the findings suggest that postprandial measures after a liquid meal are as reliable and clinically relevant as fasting measures for cardiometabolic disease research and diagnosis. Show less
