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

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.


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