In any science field, including physics, it is important to remain abreast of new assessment methods to cater to the 21st-century student. The rationale of this paper is to argue for a move away from the use of lower-order thinking skills (LOTS) in e-assessment in favor of higher-order thinking skills (HOTS), in line with Bloom's Revised Taxonomy. This builds on the work of Livingston, who argued that multiple-choice questions, while presenting some advantages, also entail disadvantages since there are forms of knowledge and skills that they cannot evaluate. This is especially true when certain forms of knowledge and skills cannot be accurately evaluated if the answer is presented within a list of options. Livingston argued that constructed-response questions are a fruitful avenue for addressing this shortcoming. Similarly, as Jones points out, while multiple-choice questions can--with careful design--be used to assess higher-order thinking, it is far more common to find them being used to test factual information recall, which requires LOTS. Schultz echoes this view and made use of randomized non-multiple-choice assignments, delivered via a Learning Management System (LMS) in a chemistry course. The benefits reported include automatic marking, reduction of copying among students due to randomization, and the targeting of higher-order learning outcomes since students were required to work out the answer rather than choosing it from a list. While Schultz did not use the term constructed-response question, Livingston defines it as "questions that require the test taker to produce the answer, rather than simply choosing it from a list." In this paper, we aim to illustrate a range of new possibilities (within physics) for using constructed-response questions in an increasingly technologically advanced learning and teaching environment. While we use the Sakai LMS, the examples we offer are equally valid for other systems. The use of constructed-response questions to support physics learning and teaching within Sakai is, however, an underresearched area. This is especially the case for the calculated and numeric response questions, and their complementary tools, that we showcase.