Learning Scaffolding in Mathematics and Statistics classrooms

Image by Ashkan Forouzani


When it comes to dealing with large heterogeneous mathematics and statistics classes, one of the best ways to ensure success of all your students is to implement learning scaffolds throughout the learning process.

The following is a short summary from one of our webinars with Dr. Dirk Tempelaar who is a senior lecturer at the School of Business and Economics at Maastricht University. During the course of the webinar, Dirk dives into the different learning scaffolds that he has implemented in his classrooms with the aid of digital technology.


Defining learning scaffolding

Learning scaffolds or scaffolding can be seen as the support structures implemented by an instructor to guide and help a student along their learning process. While there are varying classifications of what exactly constitutes as an adequate learning scaffold, each with an emphasis on a different aspect of the learning process, one of the most commonly used models boils it down to these three key characteristics:

1. Contingency

The contingency factor is referring to how the learning process is adjusted or tweaked by an expert based on the learner’s current level of ability. Every student’s learning experience is customized to account for their individual weaknesses and strengths.

2. Fading

Fading refers to these contingencies being slowly and gradually removed as a learner becomes more competent and progresses further in their learning journey. In other words, the training wheels need to eventually come off.

3. Transfer of responsibility

This trait refers to the scaffold eventually leading to the learner internalizing a new piece of knowledge or skill and consequently becoming a master. This would be when the training wheels fully come off.


Implementing learning scaffolds

Now that learning scaffolds have been sufficiently defined, we can move into the educational context in which Dirk implemented them. Dirk teaches mathematics and statistics to first year business and economics students at Maastricht University. These classes are quite heterogeneous with students coming from different schooling backgrounds both locally and internationally, which results in varying levels of mathematical proficiency. On average, we are looking at incoming cohorts of 1000 to 1200 students. One of the main reasons that Dirk decided to integrate digital technology into his lesson structure was to deal with the sheer size and diversity of his classes. The goal being to reduce the first year dropout rates by providing the students with adequate learning scaffolds during their learning journey with the help of digital technology.

While there are several different types of learning scaffolds that fit the criteria mentioned earlier in this piece, these are the three approaches that Dirk decided to move forward with when setting up his online learning environment:

Worked-out examples

This scaffold is intended for the earliest stages of mastering a skill. Many studies have found that worked out examples are the best way to introduce learners initially to a mathematical skill that they need to acquire because early problem solving attempts are otherwise usually error-prone and driven by superficial strategies.

Worked out examples

Access to endless step-by-step worked examples


Tutored-problem solving

With this scaffold, students receive feedback in the form of hints and an evaluation of their provided answers for any attempted exercise. They are provided with this feedback both during and at the end of the problem-solving steps.

Personalized feedback

Step-by-step feedback and hints

Untutored-problem solving

With this scaffold, which is often the last one a student uses before mastering a skill, feedback is restricted to the evaluation of a student’s provided answers at the end of the problem-solving process. So there is no longer hints or feedback for each step of the problem solving process but rather just feedback as to whether your answer is right or wrong. However, this scaffold still allows students to have multiple attempts at a question.


Results

When it came to results, Dirk found that the learning scaffolds were most impactful when it came to the weaker students in his class:

“The students we see in our introductory courses are extremely diverse, ranging from the high school math track that prepares science & technology studies to the high school math track that prepares social science students. There is a huge gap between these two levels. My high track students (⅓ of all my students) could in principle write the exam the first day of the course. In contrast, the low track students face a huge task: learn in 8 weeks what the other students learned in 6 years. The introduction of the tools makes it possible that the students of the lower track can write the same exam as the students of the higher track. Without the practice in the tool, this would not have been possible”

You can check out the full webinar here.

You can check out the full webinar recording on YouTube