## The Advanced Mathematics and Physics Assessments

The Advanced Mathematics Assessment

The advanced mathematics assessment is organized around two dimensions: (1) a content dimension specifying the subject matter to be assessed and (2) a cognitive dimension specifying the cognitive or thinking processes to be assessed (see the table below). TIMSS Advanced assesses student knowledge in three content domains—algebra, calculus, and geometry—which vary in the percentage of score points they represent and, therefore, in their contribution to the overall advanced mathematics scale score. TIMSS Advanced assesses students' mathematical thinking in three cognitive domains: knowing, applying, and reasoning. The cognitive domains also vary in the percentage of score points they represent. Calculator use is permitted in TIMSS Advanced.

The Physics Assessment

The physics assessment is similarly organized around two dimensions: (1) a content dimension specifying the subject matter to be assessed and (2) a cognitive dimension specifying the cognitive or thinking processes to be assessed (see the table below). TIMSS Advanced assesses student knowledge in three content domains—mechanics and thermodynamics, electricity and magnetism, and wave phenomena and atomic/nuclear physics—which vary in the percentage of score points they represent and, therefore, in their contribution to the overall physics scale score. TIMSS Advanced assesses students' scientific thinking in three cognitive domains: knowing, applying, and reasoning. The cognitive domains also vary in the percentage of score points they represent.

Table C. Percentage of TIMSS Advanced score points devoted to content and cognitive domains, by subject area: 2015

 Advanced mathematics Physics Content domains Percent of assessment Content domains Percent of assessment Algebra 35 Mechanics and thermodynamics 41 Calculus 36 Electricity and magnetism 26 Geometry 29 Wave phenomena and atomic/nuclear physics 33 Cognitive domains Percent of assessment Cognitive domains Percent of assessment Knowing 29 Knowing 27 Applying 41 Applying 44 Reasoning 30 Reasoning 29 NOTE: The percentages in this table are based on the number of score points, not the number of items. The number of score points and the number of items are not the same because some constructed-response items are worth more than one score point. (For the corresponding percentages based on the number of items, see the Methodology and Technical Notes. The content domains define the specific advanced mathematics and physics subject matter covered by the assessment, and the cognitive domains define the sets of thinking processes that students are likely to use as they engage with the respective subject's content. Each of the content domains has several topic areas. Each topic area is presented as a list of objectives covered in a majority of the participating education systems. However, the cognitive domains of advanced mathematics and physics are defined by the same three sets of expected processing behaviors—knowing, applying, and reasoning. What defines each of the processing behaviors, however, differs slightly for each subject to reflect the specific thinking skills required for advanced mathematics and for physics. Detail may not sum to totals because of rounding. SOURCE: Martin, M.O., Mullis, I.V.S., and Hooper, M. (Eds.). (2016). Methods and Procedures in TIMSS Advanced 2015. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

For more detailed descriptions of the range of the content and cognitive domains assessed in TIMSS Advanced, see the TIMSS Advanced 2015 Assessment Frameworks.