Level	General descriptors	Item-related descriptor for The 100-m race item
Critical mathematical	Text & Context: Student shows critical and questioning engagement with both familiar and unfamiliar contexts Representation: Student shows ability to summarize the association of the variables shown in the graph/table and relate it to the context Statistical-mathematical: Student performs sophisticated or critical statistical and mathematical skills, associated with mathematical concepts such as central tendency and dispersion measures	Text & Context: Student understands that choosing the best runner cannot be done in one way, it needs to consider and compare several appropriate ways; possibly interprets the data out of the provided context critically Representation: Student provides a critical interpretation of the times presented in the table for each runner; appropriately identifies trends and measure of data center Statistical-mathematical: Student is able to select the best runners by considering various statistical ideas such as mean, trend, mode, and variation; combining mean and trends; and performing accurate and sophisticated calculations
Critical	Text & Context: Student shows critical engagement with familiar context and non-critical with unfamiliar contexts Representation: Student demonstrates awareness of relevant features of graph/table and awareness of the integration of more than one relevant aspect of data Statistical-mathematical: Student shows qualitative interpretation and sophisticated use of mathematics or statistical concepts	Text & Context: Student understands the context as the previous level but can decide how to choose one runner critically Representation: Student focuses on the times of all participants (can relate the information in the table to the context to find the mean of time of the three runners); can compare the time from race to race for all three runners Statistical-mathematical: Student is able to choose one of two runners who have the same mean with further critical justification (such as the fastest record, won the most races, etc.); compares trends and interprets them from the three runners; uses of basic number sense in calculating the mean
Consistent non-critical	Text & Context: Student shows appropriate engagement with the context but often in a non-critical manner Representation: Student makes sense the data presented in graph/table with partial recognition of the context, focuses on a single relevant aspect, or compares within a data table or graph Statistical-mathematical: Student reasonably shows the application of statistical and mathematical concepts and includes those associated with graph characteristics	Text & Context: Student understands that the winner of the race is the runner who has (the shortest) time (in each race/total time); considers the time taken by a runner from race to race; considers the runner who won most often (or running with the shortest time) Representation: Student focuses on each race (finds the smallest time in each race and or after those times are added up); student compares the decreasing time from race to race of a runner Statistical-mathematical: Student only uses one of the mode/trend/total time/mean; chooses two runners who have the same mean; chooses the runner who has the lowest mean due to miscalculation
Inconsistent	Text & Context: Student shows selective or inconsistent engagement with the context (dependent to some extent on the format of the items) Representation: Student tends to interpret the graphical/tabular details rather than the context in graph/table and relate it to irrelevant contextual issues Statistical-mathematical: Student makes conclusions but may not be accompanied by suitable statistical or mathematical justifications	Text & Context: Student begins to understand (but still involves informal understanding) the context of the running competition; understand the context of selecting one out of three runners but do not understand the context of the time required by runners such as choosing the runner who wins the most (with the largest number) Representation: Student focuses on finding the winner (= the longest time) in each competition/after adding up/calculating the mean; begins to understand the meaning of the numbers on the table for each runner but it is not consistent Statistical-mathematical: Student performs errors in selecting one runner such as using the mode to select the best runner (with the greatest time); performs procedural calculations (allowing a slight error in the calculation, but still chooses the one with the greatest total time/biggest mean); Even though the understanding is correct, there is a fatal miscalculation so that the choice is wrong
Informal	Text & Context: Student shows engagement with the context but colloquial or informal (reflecting intuitive or non-statistical believe) and reflects irrelevant aspects of the context Representation: Student is able to observe the value presented in the graph/table Statistical-mathematical: Student performs basic one-step table and graph calculation (such as addition and subtraction) based on the values observed, yet sometimes with imaginative story	Text & Context: Student relates the context of choosing runners with other contexts, such as choosing the best, highest, greatest value, etc.; connects the data in the table with the strength of each runner Representation: Student focuses on finding the largest numbers from the table as a whole; interprets based on everyday/other informal understanding of the data in the table; interprets the increasing time in a positive way and the decreasing time in a negative way Statistical-mathematical: Student performs addition of certain numbers and does not relate to the question; makes a lot of miscalculations; selects a runner based on an informal contextual understanding and table reading
Idiosyncratic	Text & Context: Student shows non-existent and personal engagement with the context Representation: Student shows personal belief and experience underlying their basic graph and table reading (e.g., reading cell values) Statistical-mathematical: Student guesses the answer, makes one-to-one counting, picks a random value, selects the largest number or other unreasonable steps	Text & Context: Student skips the information in the text above the table / fails to relate the information in the text to the numbers in the table; involves personal (non-statistical) views in interpreting the context of the 100-m race Representation: Student only mentions/re-writes numbers in table without knowing their meaning; does not know the meaning of the numbers 1–7 (= the 1–7) and/or the numbers in the table (= the time required for each student); provides no results from the table reading Statistical-mathematical: Student selects one runner with no reason; does not perform any statistical and mathematical knowledge