Textbooks

From a teacher's perspective, it is important to consider how a math textbook positions students in relation to their teacher, other people and their own experience. I thought it was interesting to consider how the textbook's language can either reinforce a formal teacher/student relationship or encourage a more interactive approach. I also liked the idea to encourage students to challenge or critique the content. I was thinking about how the textbook was used in class impacting my learning experience. I remember in some classes, greatly depending on the textbook and studying it. I knew that they teacher trusted it as a main resource and that it contained almost everything I needed to know to be successful. Other of my past teachers, only seemed to use it as a resource for questions but it wasn't as central to the class routine. I often saw myself in the questions or scenarios but I imagine for many students the use of personal pronouns and modality in the textbook's language didn't make them feel included in the curriculum. Thinking about the textbook's we looked at in class, I think images and reference can help students connect to the relevance of math in real-life contexts. 

I think textbooks can be really helpful resources for some students. I do not think I want it to be central in my learning environment. I think for some students, having something tangible that isn't online is helpful. I also thinking having a compact resource where they don't have to sort through online information can be helpful. When the teacher gives some optional work, it allows students to choose how much they use the textbook. I see the benefits of using online resources - it is convenient, accessible, and there is so much to draw on! However, I also really enjoyed having a book I could write in and make my own. I am also attached to the idea of helping students reduce their screen time. In summary, I don't think textbooks are central but I think they can be helpful for some students.

Lesson Plan topic

Grade 8 Math Operations with fractions

'Flow' reflection

It was interesting to consider the benefits of having students be in a 'flow' state in class and what benefits that would elicit. I think the idea of being challenged and using existing skills is really important for a math classroom and a key role of the teacher - to find activities that are not too challenging but also not boring. 

I have experienced a state of flow -  when I am interested in completing a task I can get into a state of flow. Sometimes cooking, biking, reading or doing a Math question and I can feel very focused but enjoying my progress. I remember feeling that sometimes in Math exams - very odd I know! But if I felt well prepared, I was concentrated and just challenged enough. 

I do think it is possible to achieve a state of flow in secondary math classes but students need to have some level of interest in what they are doing and feel capable of reaching the goal. This really does depend on the culture of the classroom the teacher creates and how aware the teacher is of the level the students are at and how to challenge them just enough and pique their interests. I don't know if it is possible to have all students in "flow" all at once, but hopefully creating a culture of exploration and teamwork will allow it to happen frequently! I think the 'Thinking Classroom' design is a great way to set up a classroom where students will experience 'flow'. 

Dave Hewitt reflection

 It was interesting to watch how Dave Hewitt fostered student engagement in the video. He mentioned wanting students to be in control and he achieved this by having them answer questions about something being right and decentralizing himself. I love the idea of having students check if something is right by using problem-solving skills. I do think smaller groups are better because some might be lost but can just go along with what the collective is saying. This was a great example of how math knowledge is accessible and intrinsic. Students went from counting to the beginning of multi-step algebra! 

I enjoyed the fraction activity and I think it would work very well in a classroom. It encourages mathematical thinking and problem-solving. I appreciate how his method is very visual and how he introduces problems in context and increases difficulty slowly as to scaffold the understanding. I'm not sure how he created the fractions problem, perhaps by trial and error and working backwards from a solution? Teacher-created math problems can be great, especially when the teacher has thought through exactly what knowledge is needed and knows that students are ready for that particular problem. Sometimes textbook questions don't work for our classes because they are so general. 

Hewitt's methods remind me of the Thinking Classroom (Peter Liljedahl) because it is focused on student innovation and students being in control of their learning. He doesn't take the role of having all the knowledge but rather has students figure things out. I want to teach like this. 

Arbitrary and necessary - Nov. 6

 

Arbitrary names and labels are developed within a community. I think it is important to recognize that students come from many different communities and the labels or names that they are used to are just as effective at describing a particular shape or idea. This reminds me of conversations we have had in our LLED class about literacy and how students who are ELL have a background of knowledge in other languages and should be able to use that in conveying ideas. As teachers, we need to think about what we are assessing and give our students multiple modes to communicate their understanding. 

The author describes necessary parts of education as being things that students could figure out, that don't have to be taught like conventions or names. This makes me think of the thinking classroom and how the belief that students can actually figure out a lot of the content in the curriculum is the foundation for that pedagogy. Students are given very short lessons and then prompted to figure out a lot of things. 

One example from my practicum was how the teacher introduced the idea of radians as another way to measure angles and talked briefly about how it was developed but did not give any direct conversion between the two. The students then had to figure out how to convert in groups. I had never seen this done before, I had only seen teachers present 180/pi and then have students practice. It was so excited to students use their understanding of ratios to figure out the conversions.

There is an important discussion started here about what are we trying to teach students and the significance of doing math not just learning arbitrary steps or conventions. The skills developed in figuring things out are so much more valuable. The competencies we want students to develop can not be taught with the "recipe" format of teaching because to learn problem-solving, students need to work through things and use multiple strategies to get there.