2.4 Lesson Investigation

2.4 Lesson Investigation: The lesson included an investigative or problem-based approach to important concepts in mathematics or science.

The item assesses the degree to which investigative or problem-based instruction is successfully incorporated into the lesson. In a problem-based approach, the teacher challenges students by presenting real-world problems or realistic dilemmas to solve—often fraught with complexities requiring multiple approaches—in an effort to engage students in higher-order thinking, creativity, and innovation. An example of a problem-based lesson would be the teacher presenting a scenario to students where they are given a variety of data plans from multiple cell phone carriers and need to compare the trade-offs of features using linear functions. An investigative approach is used when students are challenged to discover important mathematical or scientific ideas, procedures, and principles through some kind of inquiry, which can be guided to open-ended in structure. An example of an investigatory science lesson would be one where students are expected to investigate causes of water pollution in a local ecosystem by determining what data need to be collected, what equipment to use to collect the data, what statistical techniques to use to analyze the date, etc.

With this indicator, it is important to assess not only if the activity was designed to be investigative or problem-based, but also whether it is enacted that way. For example, the teacher may lead the class through a problem-based scenario step-by-step with little student interaction or freedom to work on ideas or conjectures of their own, so the teacher is really just presenting an example in a lecture rather than engaging the students in problem-based learning.

It is also important when rating this indicator to distinguish between “problem-based” approaches and simply giving a bunch of problems superficially set in “real-world” contexts. In order for a lesson to be truly “investigative” or “problem-based,” there must be a larger purpose or overarching conceptual understanding that unites and gives purpose to many smaller mathematics or science problems or tasks. For example, if students were solving a variety of real-world problems using fractions to calculate food portions, this would not necessarily be a true “problem-based” lesson. However, if students were solving these problems with the larger purpose of designing a business plan for a catering company that would deliver a profit ratio that would ensure sustainability, this would then be a problem-based scenario.

Although it may seem inappropriate to penalize a teacher for not incorporating these instructional strategies into every single lesson, it is important that we identify the degree to which these behaviors are present. If there are absolutely no elements of investigation or problem-based instruction in the observed lesson, this indicator should be rated a 1. The indicator should be rated a 1 in this situation even if you feel such instructional strategies would not be appropriate or possible for this particular lesson.

General Rubric

1. This item should be rated a 1 if there were no elements of investigation or problem-based learning in the lesson.
2. This item should be rated a 2 if there was only a minor example of investigative or problem-based learning in the lesson, and it wasnot a focus of the lesson.
3. This item should be rated a 3 if elements of investigative and/or problem-based learning were designed to occur with moderate frequency, and/or if the problem-based or investigative activities were of moderate quality.
4. This item should be rated a 4 if the majority of the lesson design employed an investigative or problem-based approach and the activities planned were of medium to good quality. However, there may be a small missed opportunity on the part of the teacher to incorporate more aspects of investigation or problem-based learning into the lesson.
5. This item should be rated a 5 if the lesson was clearly designed with an investigation and problem-based approach, and the learning activities chosen were of high quality.

Specific Examples of Supporting Evidence

Science

1. The lesson structure did not include any elements of investigation or problem-based activities. The students were given a worksheet with a diagram of the water cycle and asked to fill in blanks using their textbook as a reference.
   
    
2. The lesson structure contained a few elements of an investigative approach to discover the properties of water that form the fundamental basis for the water cycle—that water changes from a solid to a liquid to a gas under differing conditions of temperature and pressure. Students were provided with phase diagrams of water and asked to correlate this information with the water cycle diagram.
   
    
3. The lesson was designed with an introductory lab activity where students were expected to determine the temperature of water as it changed from solid to liquid to gas and to draw phase diagrams based on the data they collected. The teacher then played a video “cartoon” showing the molecular structures and interactions of H₂O as it changed phases. After the video, students were asked to add similar cartoon drawings of the H₂O molecules to their water cycle diagrams.
   
    
4. The lesson was designed to begin with an investigation into the physical properties of two different substances—H₂O and lauric acid (C₁₂H₂₄O₂)—to determine the respective melting points. Student groups were then challenged to draw cartoons of each of these two molecules and describe their interactions during the melting and freezing process.
   
    
5. The lesson was designed to begin with an investigation into the physical properties of two different substances—H₂O and lauric acid (C₁₂H₂₄O₂)—to determine the respective melting points. Student groups were then challenged to draw cartoons of each of these two molecules and describe their interactions during the melting and freezing process. Finally, the groups were challenged to describe how a “water-cycle” with a liquid that had the physical properties of lauric acid would be different from what currently exists on Earth.

Mathematics

1. The lesson structure did not include any elements of investigation or problem-based activities. The teacher provided the students with a handout that listed several different representations of functions. The teacher solved example problems at the board, illustrating each of the different representations listed on the student handout while the students took notes independently at their desks.
   
    
2. The teacher made an attempt at making this lesson problem-based by framing the students’ work on the algebra worksheets as something they had to write for an imaginary company that wanted to investigate how the motion of projectiles could be approximated by quadratic functions; however, the teacher did not call attention to this prompt after the introduction and it was not mentioned again during the observation.
   
    
3. At the beginning of the lesson, the teacher had students investigate the structural properties of linear functions by giving them cards with a linear function (i.e., y = 2x + 10) and having them come up with a real-life scenario that the function could model.
   
    
4. In this math lesson, after students received a brief introduction on the use of formulas for calculating permutations and combinations, students were given a problem-based scenario where, if they needed to unlock a variety of different types of combination and permutation locks quickly, they had to decide which lock(s) would be easiest to crack. The calculations were not straightforward, and students explored this activity for the majority of the class period.
   
    
5. Students spent the entire class period working on a problem-based scenario where they had to design a playground for their community with limits on resources—money and time. This design challenge required the students to integrate both mathematics and science content and concepts.