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

Archive for the ‘O1’ Category

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.


Exceptionality in the Classroom

All students can learn. And I believe all students can learn math!



H1 – Honor student diversity and development. 

Attention Deficit Hyperactivity Disorder (ADHD) has become prevalent in the student body. As students struggle through the implications of such a disorder, it is important to recognize the behavioral and academic implications in the classroom. The article below provides some background and commonalities of ADHD as well as trends seen in the development of mathematics skills in students with ADHD.

Math Students and ADHD

Many students seem to find it difficult to transition from elementary addition of positive numbers to the addition of both positive and negative integers. And yet, this is a vital skill to learn. It is my belief that any student can develop the skills necessary and gain understanding of these concepts so as to achieve mastery in integer addition.

One important way to accomplish this is through lesson planning and the implementation of multiple learning styles. I have developed a lesson plan for the teaching visual and kinesthetic learners how to add and subtract with both positive and negative numbers.This is age appropriate for 7th grade students and meets appropriate OSPI standards as described in the lesson.

Teaching positive and negative addition to students with ADHD

Specifically, this lesson was designed with students with Attention Deficit Hyperactivity Disorder (ADHD) in mind. It is a dynamic and active lesson including games and the use of manipulatives to engage the students. In this way, students gain understanding though kinesthetic experience as well as stay engaged through visual reminders. Additionally, the lesson includes a self-monitoring sheet which allows the student to monitor his/her own behavior throughout the activities.  This creates a sense of ownership of the student’s learning which will positively influence future learning. In this lesson, we use colored chips to symbolize positive and negative numbers (as shown in the picture above). This demonstrates visually the differences between positive and negative integers allowing the student to develop a sense of “opposites”.

In writing the above article and designing the lesson plan, I have learned a great deal about the diversity of students with ADHD and how that will affect my teaching. I recognize I will need to integrate engaging activities and learning experiences in my lessons so that students are able to stay engaged. I also recognize the importance of self-monitoring aids that aid the student in developing an ownership of their behavior and learning. Though this lesson was designed for students with ADHD, it could and should be used for a wider demographic of students. It will be important in future lesson planning to consider the class being taught and the individual needs of the students. Additionally, taking advantage of other prompts and manipulatives will be key to presenting concepts to students with different learning styles.

Writing and Math?

Public writing is most definitely a valuable skill that all students should gain through their academic career. There are countless ways in which this type of writing is used later on in life. In a mathematics class however, I question the logic of incorporating larger pieces of writing and thereby reducing the amount of academic learning time spent on content specific activities. While some writing projects such as research papers can create an opportunity for students to dive deeper into content, teachers must take care to balance written communication, the learning that takes place in writing, and time spent on tedious papers.

There are several take-aways from Chapter 6 of Content-Area Writing, which, regardless of the writing assignment (public and/or long in length) I feel should be taught extensively throughout all content areas. The main take-away is to implement supportive writing by providing answers to the questions: “Why are we doing this?”, “How do you actually write this stuff?”, “What if I make a mistake or get confused?”. In answering these questions, teachers not only teach specific content and how to demonstrate their skills, they also motivate students, and create an environment conducive to learning. In this way, teachers centralize their teaching around the students.

Making Purple: A lesson in 6th grade Probability

Red+Blue = Purple !

This is a 6th grade lesson on experimental and theoretical probability. Attached are the following

1) Lesson Plan Part 1-5: Probability Lesson Plan 6th grade

2) Text pages: probability scan

3) Blank Worksheet: making purple blank worksheet