The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

Archive for May, 2013

O2- Appropriate Challenges in Math

O2- Offer appropriate challenge in the content area.


Teacher-candidates plan and/or adapt curricula that are standards driven so students develop understanding and problem-solving expertise in the content area(s) using reading, written and oral communication, and technology.

This means that as a teacher, I design and adapt my instruction, based on the standards, to give students multiple pathways of success. My instruction challenges students to use reading, written and oral communication, and technology in order to problem-solve and demonstrate their understanding.

In concluding and reviewing the topic of transformations in my 8th grade algebra class, I designed a lesson plan which gave students multiple ways of articulating their knowledge, while challenging them to work with transformations using multiple perspectives.

Transformations Lesson 5

Specifically, this lesson had the following objectives. Students will write the learning target in their journal (read/write), use the learning target to remain on task during group work (reflect/problem-solve), discuss the learning target and why it is important during the closing discussion (oral communication), and finally, demonstrate proficiency by completing the exit ticket (graphing, written communication).

Throughout the unit on transformation, you-tube videos and online graphing sites where used compliment instructional materials.


After teaching this lesson, I learned about the differences of my students’ learning styles and the methods they prefer in demonstrating their understanding. In the future, I plan to use similar strategies for effective lessons on other topics. In addition, I will use give students more freedom of choice (differentiation by interest) in demonstrating their understanding.


O1- Standards Based Curriculum

O1- Offer an organized curriculum aligned to standards and outcomes.

Teacher-candidates align instruction to the learning standards and outcomes so all students know the learning targets and their progress toward meeting them. This means that I design curriculum based on the standards and use learning targets to anchor student expectations. In doing this, I encourage students to take ownership of their own learning reflect on their progress towards meeting those standards.

In the last month of student teaching, my algebra and 8th grade classes have been going through a year-end-review. In order to give students the opportunity to self-reflect on their own understanding of key topics in their respective curriculum, I designed the instruction to cover 1-2 standards each day with an exit or entry ticket specific to those standards. As the weeks progressed, students were given a chart in which they could label the topic/standard covered, record the graded exit ticket score, and then reflect upon their own level of confidence in that topic area. Finally, the chart has a column for action steps in which students can write down one way they will improve in this standard/topic area if necessary.

Two example exit tickets are can be found in the following links.

Algebra: Transformations Exit ticket          8th Grade: Exit ticket Rational and Squared Numbers


The learning targets given during these review days were directly related to the standards. For example, in the exit ticket given for algebra students, the learning target was, “I will graph functions and describe them as transformations of the parent function.”

The standards for this lesson were, “Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.” Therefore, by asking the students to write the learning targets in their journals, complete the lesson activities, and then conclude the lesson with the exit ticket and chart, students were made aware of the standards and given the opportunity to reflect on their progress toward meeting them.

In creating this review strategy, I learned the power of encouraging students to take responsibility for their own learning and education. Students were able to get feedback on specific skills and competencies, reflect on how their scores relate to their confidence levels, and then take a course of action toward further progress.

In the future, I hope to implement this strategy as a typical review exercise and give students specific action steps to choose from so that they can grow in the areas they struggle in. In this way, I will give students further opportunity to be responsible for their learning and be less dependent on the teacher.

Extra-curricular Reflection #3

Softball Game

Walking up to the stands, I heard my name “Look, its Ms. Becker”, “Hi Ms. Becker!” I had talked with several of my math students about their softball games and determined to come see the recreational department teams play. It was great to see their enthusiasm for the game, their encouragement towards each

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other, and analyze the positions they played. I was surprised to see one student, typically distracted in my algebra class, pitch the entire second round of innings. She was focused, methodical, and very talented. She struck out many batters and ended up winning the game for her team. She did not waver under pressure and threw few balls, walking no one while I watched.

As I watched her from behind the fence, I thought, “Well, that’s it. Now I will have to expect more out of her in class.” It is interesting how an outside event affected my view of this student. Now that I knew she was capable of intense focus and drive, I felt I could use softball, or the dynamics of the game, to inspire focus and motivation in algebra. There are many aspects of math that can be applied to baseball/softball. In this way, I hope to incorporate student interest in my math lessons.

Extra-curricular Reflection #2

Teachers versus Students Volleyball

The tension built as we walked out on the court. Our adversaries were warming up with their traditional drills, their uniforms and knee pads giving them the professional edge over our mismatched bare-kneed team of teachers and interns. As we began playing, our objective was obvious- get the ball over the net. Out opponents however, as an experienced team, worked to touch the ball three times before sending it flying in our direction. While we were inexperienced and sloppy, our strategy began paying off as we kept pace with the skilled middle school girls’ team. It was teachers versus students, and it was close. Our simple but effective strategy won out in the end as the teachers won, beating the students by 7 in the last game.

images (1)This experience was awesome. At first I was nervous as I was thought dressing down would make me “less of a teacher” in the mind of my students. Instead, it seemed to humanize me to my students, showing them I was competitive and enjoyed athletics. Students and principal cheered together as both teams focused on the little white ball flying back and forth across the court. In the end, the teachers won. I didn’t like this outcome as I thought it would probably be best to let students win, since teachers had also won in the basketball game. However, the students took it well and everyone seemed to have a good time.

Extra-curricular Reflection #1

Activity Day at Middle School

6a00d8341fa9ad53ef00e54f0c5a108833-800wiOn special days at our middle school, the academic day ends early and students and teachers participate in a variety of fun activities- Activity Day! On this particular day, several tables were set up with games like “guess what’s in the box”, where students stuck their hands in a black box only to feel slimy spaghetti or Jell-O. Other tables had puzzles and board games, while the gym shook from the bass as the school dance took place. It was fun to see students relaxed and in a non-classroom setting. As I helped to direct the “guess what’s in the box” activity, I was able to connect with my students on a more personal level, joke around with them, and observe their friend groups outside the classroom. It was also helpful to see where students’ interests took them. Some students preferred to dance the whole time, while others preferred to sit at the doodle-design activity table.


Understanding students’ interests will definitely help me as I plan math lessons and activities. This will especially be helpful as I look to connect math topics with the real life experiences of my students.