National Standards and Guidelines Met through the Iron Cross Challenge
National Science Education Standards
American Association for the Advancement of Science (AAAS)
Principles and Standards for School Mathematics
National Science Education Standards
Content Standards
Standard A: Students develop the abilities necessary to do scientific inquiry and understandings about scientific inquiry.
Standard B: Students develop an understanding of motions and forces.
Standard E: Students develop abilities of technological design and understandings about science and technology.
Standard G: Students develop and understanding of science as a human endeavor and the nature of scientific knowledge.
Teaching Standards
Standard A: Teachers develop a framework of yearlong and short-term goals for students. Teachers select content and adapt and design curricula to meet the interests, knowledge, understanding, abilities, and experiences of students. Teachers select teaching and assessment strategies that support the development of student understanding and nurture a community of science learners.
Standard B: Teachers focus and support inquiry while interacting with students. Teachers orchestrate discourse among students about scientific ideas. Teachers challenge students to accept and share responsibility for their own learning. Teachers encourage and model the skills of scientific inquiry, as well as the curiosity openness to new ideas and data, and skepticism that characterize science.
Standard C: Teachers use multiple methods and systematically gather data about student understanding and ability. Teachers analyze assessment data to guide teaching and guide the students in self-assessment.
Standard D: Teachers structure the time available so that students are able to engage in extended investigations. Teachers create a setting for student work that is flexible and supportive of science inquiry. Teachers make the available science tools, materials, media, and technological resources accessible to students. Teachers identify and use resources outside the school and provide a safe working environment. Teachers engage students in designing the learning environment.
Standard E: Teachers display and demand respect for the diverse ideas, skills, and experiences of all students. Teachers enable students to have a significant voice in decisions about the content and context of their work and require students to take responsibility for the learning of all members of the community. Teachers nurture collaboration among students. Teachers model and emphasize the skills, attitude, and values of scientific inquiry.
Assessment Standards
Standard A: Assessments are deliberately designed and have explicitly stated purposes.
Standard C: Assessment tasks are authentic. Students have adequate opportunity to demonstrate their achievements.
American Association for the Advancement of Science (AAAS) Project 2061
Benchmarks for Habits of Mind
- Find answers to problems by substituting numerical values in simple algebraic formulas and judge whether the answer is reasonable by reviewing the process and checking against typical values. [solving problems in torque and Newton’s laws equations]
- Make up and write out simple algorithms for solving problems that take several steps. [analyzing the challenge question]
- Express and compare very small and very large numbers using powers-of-ten notation. [solving problems in torque and Newton’s laws and solving the grand challenge]
- Make and interpret scale drawings. [creating free body diagrams of the shoulder]
- Participate in group discussions on scientific topics by restating or summarizing accurately what others have said, asking for clarification or elaboration, and expressing alternative positions. [working in groups to analyze part of the challenge question]
Benchmarks of the Physical Setting
- The change in motion of an object is proportional to the applied force and inversely proportional to the mass. [study of Newton’s laws]
- Whenever one thing exerts a force on another, an equal amount of force is exerted back on it. [study of Newton’s laws]
Principles and Standards for School Mathematics
Number and Operations
- Develop a deeper understanding of very large and very small numbers and various representations of them [work with very small ion concentrations]
Algebra
- Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency [use algebra to solve equations of force and torque]
Geometry
- Use trigonometric relationships to determine lengths and angles [used to find lever arms, resultant muscle forces, etc.]
- Use Cartesian coordinates and other coordinates systems [plot and analyze a group of muscles on Cartesian coordinates]
- Use geometric ideas to solve problems in, and gain insights into, other disciplines [using geometry to solve a physics/biomechanics problem]
Problem Solving
- Build new mathematical knowledge through problem solving [solving the vertical iron cross problem adds to or affirms the use of trigonometry and vectors]
- Solve problems that arise in mathematics and in other contexts [using math to solve the vertical and invested iron cross problems]
Communication
- Organize and consolidate their mathematical thinking through communication [students must communicate the result of the mathematics in the iron cross problem to answer the question]
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others [vertical and inverted iron cross reports]
Representation
- Create and use representations to organize, record, and communicate mathematical ideas [use mathematical representations of forces in free body diagrams]
- Use representations to model and interpret physical, social, and mathematical phenomenon [use mathematical representations of forces in free body diagrams]