Instructional strategies employing complex problem-solving examine how learners represent the problem space and argue for decisions. Unlike problems with few solutions (e.g., multiple choices), instructors struggle to evaluate solutions to ill-structured problems quickly and consistently across students. This prevents instructors to provide timely…

The design of the formative and summative assessment processes is of paramount importance to help students avoid procrastination and guide them towards the achievement of the learning objectives that are described in the course syllabus. If the assessment processes are poorly designed the outcome can be disappointing, including high grades but…

The use of multiple-choice items for classroom testing is firmly established for many good reasons. The content any unit or course of study can be well sampled. Test scores can be reliable (trusted). And time spent administering and scoring can be minimized. This article provides a current review of best practices in the design and use of a…

Recent developments in language models, such as ChatGPT, have sparked debate. These tools can help, for example, dyslexic people, to write formal emails from a prompt and can be used by students to generate assessed work. Proponents argue that language models enhance the student experience and academic achievement. Those concerned argue that…

Classroom methods that facilitate student learning from iteration have received little attention from scholars. Iterative learning requires students to repeat a problem-solving task in new contexts each time applying lessons from previous applications. Iterative learning formats improve students' learning outcomes and help instructors ensure that…

Past research has shown that student problem-solving skills may be used to determine student final exam performance. This study reports on the relationship between student perceived problem-solving skills and academic performance in introductory programming, in formative and summative programming assessment tasks. We found that the more effective…

This article explains how high-stakes standardised tests are distorting primary school mathematics and failing to promote pupils' cognitive development. It argues for observation and journaling for both formative and summative assessment in order to recover an emphasis on reflective mathematical understanding and problem-solving.

A longitudinal study of the effects of an early childhood mathematics intervention was conducted in 2 private elementary schools in a large city in central Texas. The study included 377 participants in prekindergarten through fifth grades. Explicit non-inverted number names were taught in English and Spanish to prekindergarten and kindergarten…

In this paper we propose a method for the adaptive complex assessment (ACA) of the higher-order thinking (HOT) skills needed by students for problem solving, and we examine the impact of the method on the development of HOT skills in a problem-based learning (PBL) environment. Complexity in the assessment is provided by initial, formative, and…

This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer…

In this study, we examined the ability of grades 1-8 pre-service teachers (PSTs) to engage in thinking about patterns, relationships, and functional rules. Using the algebraic habit of mind Building Rules to Represent Functions as a framework, we examined whether and how well our PSTs (n = 18) used seven features of this habit of mind: organize…

Understanding how situational features of assessment tasks impact reasoning is important for many educational pursuits, notably the selection of curricular examples to illustrate phenomena, the design of formative and summative assessment items, and determination of whether instruction has fostered the development of abstract schemas divorced from…

In today's world, much of what used to be individual work has become collaborative. Moreover, complex change initiatives often require individuals within and across organizations to team up to set and achieve meaningful goals. The role of researchers and evaluators is to offer support that can be used to strengthen the work of organizations and…

A recent discussion involves the elaboration on possible design principles for sequences of tasks. This paper builds on three principles, as described by Bokhove and Drijvers (2012a). A model with ingredients of crises, feedback and fading of sequences with near-similar tasks can be used to address both procedural fluency and conceptual…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…