Proof Blocks: Autogradable mathematical proofs

Seth Poulsen has extended the pl-order-blocks element by adding a grading method where the dependence between the blocks is given by a directed acyclic graph (DAG), allowing many different correct orderings. This allows the construction of Proof Blocks questions, where students construct mathematical proofs by dragging and dropping blocks into a logically consistent order. Thanks go to Mahesh Viswanathan and Geoffrey Herman for design input, and Benjamin Cosman, Patrick Lin, and Yael Gertner for beta-testing Proof Blocks with their students and providing very helpful feedback.

Here is an example Proof Blocks question from an introductory proofs course:

The question.html that generates this question has:

<pl-order-blocks answers-name="proof1" source-blocks-order="random"
                grading-method="dag" solution-placement="bottom">
  <pl-answer correct="true" tag="1" depends="" > Let $m \in \mathbb{N}$ be even. </pl-answer>
  <pl-answer correct="true" tag="2" depends="" > Let $n \in \mathbb{N}$ be even. </pl-answer>
  <pl-answer correct="true" tag="3" depends="1"> Then $\exists p \in \mathbb{N}$ such that $m = 2p$</pl-answer>
  <pl-answer correct="true" tag="4" depends="2"> Then $\exists q \in \mathbb{N}$ such that $n = 2q$</pl-answer>
  <pl-answer correct="true" tag="5" depends="3,4">$m + n = 2p + 2q = 2(p + q)$</pl-answer>
  <pl-answer correct="true" tag="6" depends="5"> Since $m + n$ can be written as $2$ times a natural number,
      $m + n$ is even</pl-answer>
</pl-order-blocks>

Seth's paper Evaluating Proof Blocks Problems as Exam Questions was awarded an Honorable Mention for the best paper award at this years' International Computing Education Research Conference. In the paper, Seth showed that Proof Blocks problems give a substantial amount of information about student knowledge while being easier than written proof problems. See more research about Proof Blocks.

To try Proof Blocks, see the Proof Blocks demo question.

For more information, see the pl-order-block documentation.