4.7 Content Interconnections

4.7 Content Interconnections: Appropriate connections were made to other areas of mathematics or science and/or to other disciplines.

Connecting mathematical and scientific concepts across the disciplines tends to generalize the content and make it more coherent. A mathematics lesson on graphing quadratic equations might connect with related principles of physics. A science lesson on water cycles might connect with global warming and its economic impact on our nation. This indicator assesses the degree to which the teacher connected the mathematics or science content in the lesson to other areas of mathematics or science, or to other disciplines. For example, an algebra lesson on linear functions might connect to supply and demand in economics; a motion geometry lesson on rotation might be connected to linear functions in algebra. A chemistry lesson on the solvent properties of water might connect to an environmental science lesson on pollution of ground water from industrial wastes, the politics that gave rise to the establishment of federal agencies such as the EPA, and how understanding the chemical behavior of solvents and contaminants is applied to prevent or clean up such contamination.

Although it may seem inappropriate to penalize a teacher for not incorporating these types of connections into every single lesson they teach, it is important that we identify the degree to which these behaviors are present. If absolutely no connections between the concepts being learned and other disciplines or other areas of mathematics/science are made during the class period, this indicator should be rated a 1. The indicator should be rated a 1 in this situation even if you feel such connections would not be appropriate or possible for this particular lesson.

General Rubric

1. This item should be rated a 1 if no connections were made to other areas of mathematics/science or other academic disciplines, or if connections were made that were inappropriate or incorrect.
   
    
2. This item should be rated a 2 if a minor connection was made to another area of mathematics/science or other academic disciplines, but the teacher did not explicitly discuss this connection with the class.
   
    
3. This item should be rated a 3 if the teacher connected the content being learned to another area of mathematics/science o or other academic disciplines, and if the teacher explicitly brought this connection to students’ attention. 
   
    
4. This item should be rated a 4 if the teacher included one or more connections between the content and other areas of mathematics/science or other academic disciplines, or problems that professionals actually encounter, AND the teacher engaged the students in an extended discussion or activity relating to these connections.
   
    
5. This item should be rated a 5 if, throughout the class period, the content was taught in the context of its use in other academic disciplines, other areas of mathematics/science, or in the work of professionals, AND the teacher clearly demonstrated deep knowledge about how the content is used in those areas.

Specific Examples of Supporting Evidence

Science

1. In this lesson, students were shown step-by-step how to plug numbers from a table of hydrogen ion concentrations into a formula stored in their calculators in order to come up with the pH of an aqueous solution. There was no attempt made by the teacher to explain where the formula came from or to connect these calculations to other topics covered in the chemistry course, other sciences, or to other disciplines.
   
    
2. In this lesson, the teacher named each variable in the formula for calculating the pH of a solution and gave the students a worksheet of practice problems; some problems provided the hydrogen ion concentration and required solving for pH while others provided the pH and asked the students to calculate the hydrogen ion concentration. The worksheet had “before 1947 and after 2007” pictures of a dead fish on the shore of a lake that had been acidified by acid rain, but the teacher made only a passing reference to “what a shame” it was to see such damage.
   
    
3. The teacher opened this lesson with a short video that showed how various reactive forms of nitrogen could be produced by chemical reactions from industrial operations, over-fertilization with ammonia, and fossil fuel combustion. The video concluded with a graph showing the correlation between the rise in reactive nitrogen in the environment and the increase in acidification of soil, lakes, and atmosphere. Then the teacher provided the students with a worksheet that had them calculate the pH of different natural water, air, and soil samples where tests had determined the hydrogen ion concentration in each.
   
    
4. After showing the video described above, the teacher provided students with a diagram of the “nitrogen cycle” and discussed how the processes depicted accomplished a natural balance for nitrogen in the environment. Several students offered opinions about “how bad the chemical industry is to dump excess nitrous oxides into the atmosphere” or “how we need to stop burning fossil fuels to generate electricity.” The teacher accepted all opinions as valid but suggested that eliminating the chemical industry or all fossil fuel power plants tomorrow would not be realistic. She asked the students to solve several problems given either hydrogen ion concentrations or pH of soil, water, and atmospheric data from the EPA website.
   
    
5. The teacher opened class with a video described above, and then provided students with a diagram of the nitrogen cycle, including chemical names, general formulas, and some reactions that occur at each phase. The teacher assigned a different component of the nitrogen cycle to each group of students, and then had them use the EPA website and other web resources to research reactive forms of nitrogen and the chemical reactions they impact in the nitrogen cycle. Not only did the students have to calculate the pH of soil, water, or atmospheric samples from EPA—test data of hydrogen ion concentration—they were challenged to calculate pH and determine what would happen with the reactions in their component of the cycle if the hydrogen ion concentrations increased 10-fold, 20-fold or 50-fold. The teacher prompted students to remember what they had learned in a previous unit on chemical equilibrium and dynamics when making their predictions of impact.

Mathematics

1. In this lesson, students procedurally learned how to multiply matrices. There was no connection to other areas of mathematics or to other disciplines.
   
    
2. This was a lesson on quadratic functions, and there were two application problems that connected to motion in physics with a ball being thrown into the air. However, the teacher worked these problems just like any other problems on quadratic functions, mainly ignoring the context and its connection to another discipline.
   
    
3. The teacher connected the content in this algebra class to concepts in economics by doing a launch activity where he showed supply and demand lines. The remainder of the problems the students worked was not anchored in a context.
   
    
4. In this lesson, concepts from algebra were applied to concepts in physics by looking at Boolean algebra in circuits; the class did an activity where they explored some circuits.
   
    
5. This project was situated in the context of making a variety of math- and science-related decisions about building an outdoor theater for the community. Students integrated concepts from physics, geometry, biology, and algebra into a large design project.