Analysis of Alignment

Part 2: Alignment of Curriculum and Instruction

Background Information

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Ms. Trinh's 7th Grade Pre-AP Class

TEKS in This Lesson:

“Big Idea” Standards:

8(7) Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to:

(B) use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;

Process Standards:

8(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) Apply mathematics to problems arising in everyday life, society, and the workplace;

(B) Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

(F) Analyze mathematical relationships to connect and communicate mathematical ideas;

About the Class:

Ms. Trinh's 4th period pre-AP 7th grade class is one of the largest 7th grade math classes on our campus. The 36 students who were placed in this class are learning 8th grade math content and will be taking the 8th grade math STAAR test this May. Due to the lunch schedule on campus this class is split into two sections: one before lunch and one after. Ms. Trinh, in anticipation of my observation, changed the routine for her students to allow for me to observe note-taking and lecturing during my lunch period. Typically students spend the first half of class reviewing homework problems from the night before and the latter portion discussing new material for the day. The topic of the lesson I observed today was surface area of cylinders.

My Observations

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I Noticed:

During my 30 minute observation I closely watched the interactions between the students, the teacher, and the lecture notes. I noticed the following:

  • The initial warm-up was covered very quickly, without much dialogue from the students. I was not sure when this material had been taught or if it was on the prior day's quiz.
  • The warm-up seemed to be very teacher-led with little to no student input and feedback while the instructor was reviewing. Since I am not in Ms. Trinh's class on a regular basis I am not sure what her classroom procedures are regarding warm-ups and if the students are expected to complete the bell-ringer prior to class officially starting.
  • Most of the instruction was teacher-centered, with short pauses for student response, such as identifying what formula to use for the problems discussed using their provided formula charts.
  • Students used their graphing calculators for all mathematical computations, no matter how small.
  • Ms. Trinh walked her students through specific steps she uses herself to solve the types of problems presented in the lecture.
  • The instructor used tangible manipulatives to demonstrate the concepts of lateral and total surface area to students (Ms. Trinh used a food can and a piece of paper to show students the difference between lateral and total surface areas.)
  • The presentation of lecture materials was very static with most of the talking done by the teacher.
  • Ms. Trinh was very nervous that I was observing her classroom, and the students, many of whom we share, were overly excited to speak with me during instruction time.

I Wonder:

Since I am not always in Ms. Trinh's class (and I have never observed her class before) I am left with many questions. As a result of this observation I wonder:

  • Are all lectures given in the same manner, with the instructor providing information in a very direct, static manner, and students taking notes in their provided worksheets? How does the data reflect that students are actively engaged in the lesson and making connections back to prior content/understandings?
  • What problem is this lecture attempting to solve (ie: do students already know this concept and they needed to review or is this a brand new idea) and how does the data collected during this class, if any, support a deeper understanding into this problem?
  • How does Ms. Trinh know, in the moment, if students are really understanding concepts? How does this fit into the Theory of Action's idea of "high quality data"?
  • What forms of remediation take place in this classroom on a daily basis?
  • How does this concept (surface area) relate back to real-life examples that are applicable in the workplace? How do we know what the students' prior knowledge that relates to this information?
  • What type of independent and guided practice do students do in this class? How are the homework problems worked into the structure of the class?
  • How do students internalize formulas and the "why" behind them if they are using formula sheets exclusively?
  • Does using a calculator hinder students problem solving and higher level thinking skills?
  • What other ways could students use to communicate their understanding of this concept? Does the teacher incorporate other types of activities for her students that allow them to discuss and communicate their understandings? How are changes made in line with the Theory of Action to reflect the process standard's idea for students to communicate about math?
  • What techniques can be used to help observation-shy teachers feel comfortable with someone observing their teaching and class? Is there anything I could've done differently to lessen Ms. Trinh's discomfort with my observation?
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Action to Take:

As stated in my last review of the alignment between curriculum and assessment, I feel that the following recommendations still are applicable:

  • More emphasis needs to be placed on discussing the prior understandings that students have in regards to this material before proceeding further. If the teacher and students do not accurately know their false beliefs and misunderstandings before learning new material the priorly held understandings become permanent (Bransford, 2000).
  • Additionally, formative assessments, such as sample problems completed by students independently or in pairs, or open-ended questions that probe student understanding need to be a larger part of the note-taking experience to help create a wider range of data for the instructor to gain information from (Hess & Mehta, 2013).
  • While observing I was not able to determine which students were truly actively engaged. Datnow's (2015) five principles for equitable data use details the need to understand how engaged students are in their daily activities in school as a pathway to developing sound, relevant professional development for teachers. I propose a professional development workshop that explicitly teaches Multiple ways of teaching the information, such as pairing and sharing, inquiry based activities using real-world materials, and interactive, engaging discussions that involve all students are in dire need.

Possible Consequences:

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Bransford, J., National Research Council (U.S.)., & National Research Council (U.S.). (2000). How people learn: Brain, mind, experience, and school. Washington, D.C: National Academy Press.

Datnow, A., & Park, V. (2015). Data Use--For Equity. Educational Leadership, 72(5), 48-54.

Hess, F. M., & Mehta, J. (2013). Data: No Deus ex Machina. Educational Leadership, 70(5), 71-75.