In the video, “A Private Universe”, some of the challenges or scientific misconceptions that Heather holds are as follows:

- She believes the earth travels in a curly orbit around the sun;
- She cannot identify direct and indirect rays;
- She misunderstands the shadow of the earth.

Heather’s theories were a result of what she had learned on her own in the past. Her misconception about the orbit, for example, was based on an illustration she had seen in a textbook. In an effort to explain her theories, Heather uses illustrations and objects. Direct instruction helps alter some of her personal theories. Probing questions from the classroom teacher, along with a model of the earth, the moon and the sun, help students overcome some of their misconceptions.

One of the challenging concepts that I had in math when I was in school was comprehending word problems. I lacked confidence in math, and I used to feel stressed out when I tried to tackle word problems. I would need to read the word problem multiple times, and would have difficulty comprehending what I was being asked to calculate. I could not seem to be able to figure out how to convert the problem to numbers or a mathematical equation. In an effort to try and figure out what I was trying to solve, I would draw pictures and charts. I had great difficulty connecting what I was reading to concrete mathematical concepts.

Driver et al (1994) and Cobb (1994) draw connections between constructivism and learning science and math. According to Driver et al (1994), individuals construct their own scientific theories as a result of the interactions they have in their personal lives. Students should be able to participate in classroom activities that challenge these prior misconceptions, so that students are able to modify their knowledge. Cobb (1994) describes the process of actively drawing upon your personal experiences in an effort to construct an understanding of mathematical principles. This personal knowledge can conflict with what is being taught by the classroom teacher. Cobb (1994) also presents the sociocultural perspective whereby an individual is influenced by the “participation in encompassing cultural practices” (Cobb, 1994, p. 13).

I think it is important to present concepts in math and science using a variety of mediums in an effort to better meet the needs of different learners, and help reinforce what is being presented in the classroom. It is important for students to be engaged and have the opportunity for reflection and practice. Some of the faculty members I worked with in the post-secondary system utilized the flipped classroom model, so that lectures were recorded, and viewed by students in advance of the lesson, and classroom time was spent working on interactive, engaging activities that reinforced the concepts presented in the lecture. Khan Academy is also utilized by many teachers as an opportunity to reinforce what is being taught in the classroom. Another approach I have seen in an online learning environment is to have students create instructional videos that highlight specific mathematical or scientific concepts. These videos are added to an online resource database within the learning management system for current and future students.

**Resources**

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. *Educational Researcher, 23* (7), 13-20.

Driver, R., Asoko, H., Leach, J., Mortimer, E. & Scott, P. Constructing scientific knowledge in the classroom. *Educational Researcher, 23* (5), 5-11.

Harvard-Smithsonian Center for Astrophysics (Producer). (1987). A Private Universe [online video]. Retrieved 6 January, 2017, from: http://learner.org/vod/vod_window.html?pid=9

I struggled with the same issues in math class. Word problems were always so challenging. I think it’s important for us teachers to figure out what students already know before going forward and expanding on a given topic. Some students may have a pretty good baseline, but others may need extra help connecting all of the scattered pieces.