Chapter 7 is all about using assessment to guide instruction. In a way, this chapter merges backwards by design with involving students in assessment because it involves going through the process of thinking about the product and ways to reach it with the students’ input . At the start of the chapter Davies explains, “daily involvement in classroom assessment builds a strong foundation for learning” (p.63). This foundation is crucial in helping a student succeed. I find, even in university classes, when I am involved in the process of building an assessment (even on Monday when building the rubric for our assignment) it helps me to understand what is expected of me. Therefore, I can begin to shape ideas about what my assignment will need in order to meet the required outcome. Much of this chapter gives many examples of ways to incorporate students in the assessment *for* their learning, and indicates that it will greatly improve their product (sometimes assessment *of *learning).

One passage that resonated with me was, “educators are teaching students *how to learn* as well as what they need to know and be able to do” (p. 71). This passage hit home for me because it helped me to come to the realization that at the end of the day, students will not remember everything that we have taught them, but if we can teach them how to learn, that is a skill that they will use for the rest of their lives. If we can get our students to take some responsibility (*TPSR*, Don Hellison) for their own learning, in turn helping them to discover how they learn best, we can help them to become lifelong learners in whatever they choose. Once we have taught them the foundational skills needed to learn, the door of opportunity is flung wide open. Therefore, as teachers we have the key to help unlock our students’ potential. A HUGE opportunity.

Chapter 8 discusses ways to help your students gather evidence of their own learning. It lays out a process to follow that will help your students understand what is needed of them, and why. For this concept to work it is important that your students see the value in gathering evidence of their own learning, otherwise it will not work. It then gives examples of ways students can gather this evidence through the use of various types of portfolios. It also discusses the importance of parent involvement because, “receiving feedback from people whose opinion they value can increase not only students’ motivation but also their learning” (p.83). I think that this is a great idea that I would like to try in my future classroom. It will be very important to have parents/guardians/role models of the students that want to be involved in their learning process, otherwise the process would only work through having feedback from the teacher (maybe other students as well) and may not reach the potential it could have.

I really liked your discussion of how important it is to begin with the end in mind and to involve the students in the assessment. I’m sure that there are many in our classes who have experienced the pains of not having clear expectations on an assignment. Just recently in one of my EMTH classes, our entire class was shocked to see some of the elements which our professor had emphasized on the rubric, as we were only shown the rubric once it had our assignment evaluation highlighted upon it. By instead involving the students in the creation of the rubric or other evaluation tool we can create a better sense of transparency, and can establish more student commitment to the requirements that are given to them.

I quite enjoyed your comments regarding our responsibility for teaching our students how to learn rather than just teaching them to memorize the content. In order to complete the case studies assignment I found myself reading a lot of articles about the use of inquiry methods in both math and science classrooms, and in almost every article they stressed the importance of teaching students the process of inquiry as a technique that they will be able to use in their learning for the rest of their lives. A few of these articles in particular were:

• Nadelson, L. S. (2009). How Can True Inquiry Happen in K-16 Science Education?. Science Educator, 18(1), 48.

• Banchi, H., & Bell, R. (2008). The many levels of inquiry. Science and children, 46(2), 26.

• Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical thinking and learning, 10(4), 313-340.

For me, Chapter 8’s discussions of portfolios was one that was quite interesting. I have always found myself to be somewhat skeptical of the application of a portfolio to a mathematics course, but upon reading this I found myself somewhat inspired. In particular I found the portfolio which had four separate sections to be particularly interesting. In the past few weeks in one of my other courses we have been talking at length about the importance of having diversity in assessment in math, and we did some reading about the variety of methods of assessment which can be easily implemented in a mathematics course. I was thinking that it might be interesting to implement a set of these assessments into a portfolio type of collection, with a tab being for journaling, another for projects, one for quizzes and tests, and one for visual representations (printed pictures) of physical tasks or problem recreations done by the students. For me this really stood out as a great way to encourage the students to take pride in their work and to encourage the parents to take an active interest in their children’s education. Students place a very significant weight on both feedback from their teachers and their parents, and I feel like this would be a very easy way to engage the parents in giving their children the feedback that they need to feel motivated to continue to push themselves towards academic success.

My Math Assessment Textbook: Mathematics Assessment: A Practical Handbook for Grades 9-12 (National Council of Teachers of Mathematics (NCTM), 1999).

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