There are two types of understanding when it comes to learning math: procedural understanding and conceptual understanding. I grew up with a rigorous learning curriculum and learned math through endless drills and practices. I was less motivated to understand the reason behind those procedures. I think both types of understanding are equally important in learning mathematics. Procedural fluency is the "ability to apply procedures accurately, efficiently, and flexibly... to build or modify procedures from other procedures" (National Council of Teachers of Mathematics, 2015). Procedural understanding may perceive as merely about the understanding of the arithmetic and memorizing the steps with no understanding but in reality, students need to decide which procedure to use for a given situation; here is where the conceptual understanding comes in handy. Students need the skills to integrate concepts and procedures to develop their own ways to solve a problem, they need to know how to do it and why they do it that way. The purpose of this 5-day unit is teaching with conceptual understanding through hands-on activities and the use of tools to learn geometry. Through these lesson plans, students should be able to develop the conceptual understanding of the angles created by parallel lines and transversal, interior and exterior angles of triangles and polygons, and the use of similar triangles, while developing the procedural understanding. These lesson plans are created to align with the eighth grade Common Core Standards. Students are learning angles through the use of protractor and patty paper, making a conjecture based on their data and experience, and real-life problem solving. The lesson plans used the direct instruction and the 5E inquiry template from the iTeachAZ program. The direct instruction lesson plan includes instructional input, guided practice and individual practice. The 5E inquiry lesson plan has five sections: engage, explore, explain, elaborate and evaluate.

There is still a major underrepresentation of females in STEM fields, with many girls beginning to lose interest as early as middle school. This is due to a variety of factors including lack of role models, stereotypes, ineffective teaching methods, and peer influence. A popular way to increase female interest is through day camps and other programs where girls complete a variety of activities related to science and engineering. These activities are usually designed around problem-based learning, a student-lead approach to teaching that requires students to work collaboratively and use background knowledge to solve some sort of given problem. In this project, a day camp for middle school girls was created and implemented to increase student interest in STEM through three problem-based learning activities. By analyzing survey data, it was concluded that the camp was successful in increasing interest and changing participants' attitudes towards science. This approach to learning could be applied to other subject areas, including mathematics, to increase the interest of both male and female students at the secondary level.

Teamwork and project management (TPM) tools are important components of sustainability science curricula designed using problem- and project-base learning (PPBL). Tools are additional materials, beyond lectures, readings, and assignments, that structure and facilitate students' learning; they can enhance student teams' ability to complete projects and achieve learning outcomes and, if instructors can find appropriate existing tools, can reduce time needed for class design and preparation. This research uses a case study approach to evaluate the effectiveness of five TPM tools in two Arizona State University (ASU) sustainability classes: an introductory (100-level) and a capstone (400-level) class. Data was collected from student evaluations and instructor observations in both classes during Spring 2013 and qualitatively analyzed to identify patterns in tool use and effectiveness. Results suggest how instructors might improve tool effectiveness in other sustainability classes. Work plans and meeting agendas were the most effective TPM tools in the 100-level class, while work plans and codes of collaboration were most effective at the 400 level. Common factors in tool effectiveness include active use and integration of tools into class activities. Suggestions for improving tool effectiveness at both levels include introducing tools earlier in the course, incorporating tools into activities, and helping students link a tool's value to sustainability problem-solving competence. Polling students on prior use and incorporating tool use into project assignments may increase 100 level tool effectiveness; and at the 400 level, improvements may be achieved by introducing tools earlier and coaching students to select, find, and develop relevant tools.