When von Glasersfeld said constructing knowledge, he means the students have to create what they come to know. When a student listens to a lecture they do not take in exactly what the teacher said. The student filters the information and constructs it into knowledge based on how they saw the information through their OWN lens. Von Glasersfeld did not call this aquiring knowledge or gaining knowledge because the student doesn't actually take in what the teacher said. They take in what they thought they heard. It's usually wrong...or as Dr Seibert suggested, viable; however it is not correct knowledge because it is simply how that particular student interpreted what they heard.
If I believed in constructivism I would have a hard time seeing what my students gained from my class/lectures. So in order to work with that problem I would have my students write in math journals. At the end of each class period the students will take about 5 minutes to write what new things they learned and explain to me how they understood it. They can also ask questions etc. As a constructivist I don't believe students actually "aquire" what I have tried to teach. They construct their own knowledge so in order to better teach them I would use journals to properly assess what the students have constructed about the material. This way I can reclarify what was misunderstood and I can keep tabs on my students' knowledge.