{'fraction_non_alphanumeric': 0.03176341730558598, 'fraction_numerical': 0.01533406352683461, 'mean_word_length': 5.052980132450331, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Students ’ perceptions of functions articulated in dynamic microworlds

The use of different representations in mathematics teaching is put forward by Lesh et al (1987) and Arcavi & Nachmias (1989) as a way to help students improve their perceptions of mathematical concepts. Arcavi & Nachmias (1989) analysed pupils and adults who were considered to be mathematically expert exploring a non-conventional representation. They observed that these individuals started to re-examine their previous perceptions in familiar representations — algebraic and Cartesian. “The role of a representation of a mathematical idea seems to go beyond the mere goal of having a tool to handle that idea. Could it not be that by introducing a new representation, we are not only establishing a way to express an idea or a concept, but also re-examining and consequently learning “more” about those ideas and concepts” (Op.cit.: 84)?