%0 Conference Paper %1 Küchemann05 %A Küchemann, Dietmar %A Hoyles, Celia %B The Fourth Conference of the European Society for Research in Mathematics Education (CERME 4) %C Spain %D 2005 %E Bosch, Marianna %K as_conv divisibility factorial ijtme2006 mythesis sequences %P 438 - 447 %T Pupils' Awareness of Structure on Two Number / Algebra Questions %U http://www.mathsmed.co.uk/ioe-proof/dek-chCERME4-2005.pdf %X A large sample of high attaining pupils were given a written proof test in Yr 8 (age 13.5 years) and similar tests in Yrs 9 and 10. We look at their responses to two number/algebra questions which were designed to assess whether pupils used empirical or structural reasoning. We found that the use of structural reasoning increased over the years, albeit at a modest rate, but that the use of empirical reasoning, in the form of inappropriate number pattern spotting or through the desire to perform rather than analyse a calculation, was still widespread. However, we also identified a more advanced use of empirical reasoning, namely to check the validity of a structural argument.

@inproceedings{Küchemann05, abstract = {A large sample of high attaining pupils were given a written proof test in Yr 8 (age 13.5 years) and similar tests in Yrs 9 and 10. We look at their responses to two number/algebra questions which were designed to assess whether pupils used empirical or structural reasoning. We found that the use of structural reasoning increased over the years, albeit at a modest rate, but that the use of empirical reasoning, in the form of inappropriate number pattern spotting or through the desire to perform rather than analyse a calculation, was still widespread. However, we also identified a more advanced use of empirical reasoning, namely to check the validity of a structural argument.}, added-at = {2010-08-05T08:07:39.000+0200}, address = {Spain}, author = {Küchemann, Dietmar and Hoyles, Celia}, biburl = {https://www.bibsonomy.org/bibtex/26cf13d9d1fae69173ff322f4bf0dcafd/yish}, booktitle = {The Fourth Conference of the European Society for Research in Mathematics Education (CERME 4)}, editor = {Bosch, Marianna}, interhash = {75a599d0f3f88005473d85ba0c2ec111}, intrahash = {6cf13d9d1fae69173ff322f4bf0dcafd}, keywords = {as_conv divisibility factorial ijtme2006 mythesis sequences}, pages = {438 - 447}, timestamp = {2010-08-05T08:07:39.000+0200}, title = {Pupils' Awareness of Structure on Two Number / Algebra Questions}, url = {http://www.mathsmed.co.uk/ioe-proof/dek-chCERME4-2005.pdf}, year = 2005 }