Expanding Your Curriculum Knowledge Beyond High School

Secondary school teachers are often well versed in understanding the components of the grade 9-12 mathematics curriculum's and how to develop lessons that address each of the curriculum requirements. One component that is often overlooked by high school teachers, especially those teaching grade 9 mathematics classes, is delving into the elementary mathematics curriculum. This gives teachers an understanding of where our students are coming from and an idea of the knowledge that they have likely already obtained.

It is important for teachers to understand the knowledge basis from which our students are coming from. This allows us to develop effective lessons that will scaffold on the previous knowledge that the students have already obtained in elementary level mathematics.

During assessment it could also be noted that students may be struggling with a certain concept. This could be due to the lack of prerequisite knowledge in a certain topic from elementary which is hindering students progress in learning new material. Although not part of the high school curriculum it is your role as a teacher to ensure each student is achieving their individual successes, which may require you giving a brief lesson on elementary level topics to refresh student's minds on certain topics.

In our class this week we were given curriculum expectations for grades 7-9 and tried to develop continuum's that would link concept ideas across each grade. This proved to be a challenging task as not all of the topics made direct correlations, especially when going from grade 8 to 9. This showed how big the gap was between content in grade 9 and and elementary, which is why it is important that teachers teaching that grade should become familiar with the elementary level content.

Continnum chart linking curriculum expectations from grades 7-9.

There is also a variety of resources available on Edugains that link curriculum expectations across the grades.

First Teaching Block

For my first teaching block I was teaching the light and geometric optics unit of a grade 10 academic science class. During the practicum I learned many new skills and strategies that could be applied to any type of classroom. In this post I will talk about some of the experiences I had while on my teaching block as well as some of the challenges and difficulties that I had to overcome.

This practicum was the first time I had taught in a classroom setting. I had some tutoring and coaching experience but had never run a classroom before. One of the first challenges I encountered while teaching was pacing. Due to being in a university style setting for the past 4 years, my pacing was a little bit too fast at the beginning of block but as I gained more experience the pacing became much better and was definitely one of my biggest improvements.

Being organized was extremely important during the first block. I learned many strategies that I would use in a future classroom to help keep everything organized within the classroom. One of the key organizational strategies that my teacher used was a binder that was always within the classroom that contained extra notes/worksheets. It was the students responsibility if they missed a lesson or multiple lessons to pick-up the notes/worksheets they are missing from the binder which was organized by date of the notes and divided by each class as well. This made it much easier for putting student's who had missed days back on track.

Having an academic class, classroom management and behaviour was not a huge issue for me. Some students would be a little rowdy at times but I found that proximity during lessons and changing pace often would quiet them down.

Although I wasn't teaching a mathematics course there was still some math involved in the optics unit. The mirror equation shown above was one of the equations we would use in the class to find the distance of an image produced in a mirror. It was interesting to see how all of the students had different math capabilities within the class. I broke down each question step by step and included the class when solving problems to help cater to all of the different leveled math learners within the class. We also did a lab which had a component that applied the equation which the students found useful!

Image retrieved from: http://previews.123rf.com/images/alexraths/alexraths1209/alexraths120900001/15134543-Teacher-with-a-group-of-high-school-students-in-classroom-Stock-Photo.jpg

Overall I found my first block to be very successful. I learned many useful skills that I could use in any future classroom and gained the valuable experience of teaching in a real classroom. Can't wait until my next practicum!

Online Session Reflections

Online Session 1

In the first part of the online session we looked at Five Practices for facilitating mathematical discussions around cognitively demanding tasks within the classroom. As a beginning teacher I found that some of these tasks may be a bit challenging for me such as anticipating likely student responses. Because we are all different learners there are students in my class that will likely think of different ways to solve mathematical problems I present that I did not think about. This is perfectly acceptable but as a beginning teacher I may find it more difficult to anticipate all of the student responses to questions due to my lack of experience as a teacher. With more experience though and getting to know my students better it will make it easier to anticipate individual student's responses to questions.

I find the Five Practices beneficial for the classroom because they provide a student-centered approach to learning that creates a more dynamic and engaging classroom. For example, one of the practices is selecting students to present their mathematical responses. This can be beneficial because it shows student's how their peers solve mathematical problems and in an ideal classroom where there is no judging other students you can also occasionally select students with a common error in their formulation of their solution to the problem which can generate discussion as well as enlighten other students who had made the same mistake.

The second part of the first online module challenged us to think outside the box by solving problems using different approaches that students may use. This exercise was useful because it challenged me to use different approaches to solving a problem then what I would normally be used to which is good preparation for when I will have to anticipate student's responses to math problems while teaching.

Online Session 2

Formative assessment is important tool used to determine the level of understanding students have on certain topics/concepts/ideas. There are different ways that you can approach using formative assessment but there are five key universal steps that can be used to help achieve effective formative assessment. One of these steps is sharing learning goals with the students. This allows the students to have an idea of what they should learn at the end of a lesson so that they can asked themselves "did I achieve the learning goal today?" Another very important step is providing feedback that moves learning forward. Feedback can be provided in written, oral or through a demonstration and should force students to engage cognitively about their own work.

Written feedback to a student should provide a question to the student rather than just a "correct" or "incorrect." You should provide the student with a reasoning for why their answer was good or incorrect that allows them to think about other options or methods. For example in a substitution/elimination problem that a student solves using substitution only you may write down as feedback "great answer! can you think of another method that you can use to solve the problem?"

The teacher should also guide student's using feedback rather than providing them with the correct answer right away. This allows students to think back to the problem rather than just seeing the correct answer and moving on.


Another important thing with feedback that I believe is very important is providing enough time for students to read and think about their feedback. You can provide students with feedback on an assignment or test and tell them to read the feedback and they may or may not do so. Providing time in class to look at the feedback makes it more likely that student's will look at their feedback and cognitively engage in it.

Overall I believe feedback is important tool for all students whether they are struggling or excelling at a topic it can be beneficial for both those types of students if used effectively and this module was a great way of thinking about feedback and how it can be used in a math classroom effectively.