By Colleen Heberlein

As Brahier (2013) states, “one of the things that good teachers of mathematics do is reflect on the effectiveness of their lessons” (p. 163). Without the important piece of reflection, a good lesson will never be great and an ineffective lesson could be carried on to the next year with little or no changes. In my lesson, I set out to teach my Bridge Math students the important life skill of fluently calculating elapsed time as part of our unit on addition and subtraction. I used common, real-world scenarios from the National Council of Teachers of Mathematics (NCTM) Illuminations website almost exclusively to teach and practice the skill with students because I wanted them to apply this skill in their everyday lives. This skill is aligned to Common Core State Standard 3.MD.1 (Common Core State Standards Initiative, 2016) and NCTM Content Standard 4 (Brahier, p.77).

To measure my success in reaching that goal, students completed an exit ticket to close the lesson. Ten out of my fourteen students, or 71%, completely mastered the exit ticket. Three students showed some understanding but with misconceptions about calculating elapsed time over the hour, and one student showed very little understanding of the concept. This data tells me that my students were very close to reaching the lesson’s goal, so a whole-group reteach is not necessary. I will continue to incorporate elapsed time problems into Do Now’s in the remaining lessons for the unit.

After the lesson, I was discussing how I wish I extended the lesson past digital clocks to analog clocks with my coach, because in my interactions with students I have noticed that they struggle to read the analog clocks on the classroom walls. My coach informed me that we have clock manipulatives in the teacher workroom that I could have used. Though I wish I had asked before the lesson, I will now use these manipulatives to extend the learning from this lesson throughout the unit. Another teaching practice that I need to work on is lesson imaging, “the sense that a teacher carries into the classroom of what to expect from students, how they are likely to react, and what the teacher can do to make the lesson work” (Brahier, p. 163). I did not fully picture the lesson in my head, so during the transition from guided to independent practice, time was wasted because my instructions were not clear. I also did not fully prepare for the misconception that many students had that they could simply add the hours and minutes in the same way that we add multi-digit integers, so I did not prepare an adequate explanation for that idea. In future lessons, including when I teach this lesson next year, I will have a better mental image of how the lesson will proceed which will make the lesson and my teaching stronger.

Planning this lesson also taught me that I do not use outside planning resources enough. I tend to think that I must make lessons completely on my own, even though many teachers have taught my same subject before me. This class offered great planning resources that I will continue to reference and implement in my classroom. Brahier (2013) writes that, “although some of these best lessons can be found in resource books or on the Internet, teachers begin to ‘own’ a lesson only after planning, teaching, reflecting on, and reteaching it” (p. 164). I can make a lesson my own even if the lesson was not originally made by me by utilizing lesson imaging and reflecting on the lesson in order to continuously improve my teaching for my students.

**References**

Brahier, D. (2013). *Teaching secondary and middle school mathematics* (4th ed.). Upper Saddle River, NJ: Pearson.

Common Core State Standards Initiative. (2016). *Mathematics Standards*. Retrieved from http://www.corestandards.org/Math/**.**

National Council of Teachers of Mathematics. (2016). *Elapsed Time: Using a Timeline to **Determine Elapsed Time*. Retrieved from http://illuminations.nctm.org/Lesson.aspx?id=3966.

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