Aligning Outcomes, Assessments, and Activities

 

3 Column Table

 

BHAG (Big Hairy Audacious Goal)

Learners will collaboratively create a catapult using supplies of their choice that they will be able to accurately predict the location of a given projectile by using the properties of quadratic functions.

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Learning Environment & Situational Factors to Consider

1. Specific Context of the Teaching/Learning Situation

This is an Honors Algebra 2 course at Wissahickon High School. I have two sections of this course with 48 students total, made up of 9th, 10th, and 11th grade students.

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The class meets 4 out of every 6 days, three of which are 58-minute classes, one of which is a 90-minute block period.

The course will be delivered live, however, will typically take on a blended learning model with occasional labs.

A lack of time and the infrequencies in meeting times/days due to scheduling could affect these classes. Additionally, the strict timeline for assessments from a district level may restrict the time that can be spent on projects, labs, and discoveries.    

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Learners will rely heavily on their laptops (one-to-one in place), phones, and graphing calculators.

 

2. General Context of the Learning Situation

The district requires all Honors Algebra 2 courses to be formatted the same way, that is, assessments must be consistent from course-to-course, from timeline to points.

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Each marking period must cover two units, each consisting of two/three quizzes and a unit test. After the first semester, there is a district-assigned midterm exam covering the first half of the year, and after the second semester there is a final exam covering the second half of the year. My district is very data-driven and focused on formal summative assessments and consistency across all sections.

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In the world of secondary education mathematics, there is a focus on a transition to project-based learning and hands-on activities allowing the learners to truly interact with the content in an authentic manner. This is a focus in my course as well, however, difficult to implement due to our curriculum.

 

3. Nature of the Subject

Algebra 2 is a combination of theoretical and practical. In an honors level course, we certainly put a focus on the theoretical components to go deeper into the why of the content.

 

4. Characteristics of the Learners

Wissahickon is an extremely diverse school district with a wide variety of socio-economic statuses and cultures. This course specifically mirrors the overall make-up of the district with students coming from all different backgrounds. Most, if not all, students plan to attend a four-year college upon completing high school.

 

This honors level course is commonly known as the first challenging mathematics course that the district offers and is viewed as the “weeding out” course by students. Many 9th grade students struggle early on in this course to adjust to the pace and rigor; however, substantial growth can be seen throughout the first semester.

 

The prior course to this is Geometry, which does not have much application of Algebra 2 content, so it is important that students have a strong foundation of Algebra 1 from middle school.

 

Unfortunately, many students enter this course focused solely on grades and academic achievement rather than truly learning the content and interacting with the material in an authentic manner. There is often a significant amount of pressure from parents based around GPA.

 

5. Characteristics of the Teacher

As the learning facilitator in the classroom, my focus is on my students developing a deep, conceptual understanding of the content where they see value in what they are learning.

 

I put an emphasis on collaboration, problem-solving, and critical thinking in the classroom and prioritize open discussion between my students. I am fully aware that some of the content in the curriculum does not have very much real-life application, but it is a still a way for students to think outside the box towards a common goal.

 

I am very passionate and confident about the content that I teach and the value that it has in my students’ journey. Outside of the material, I focus on building strong relationships with my students and earning their trust to serve as a guide in their learning. I take pride in my ability to develop a classroom setting where students feel comfortable taking academic risks and participating in open conversations with one another.

 

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Questions for Formulating Significant Learning Goals

 

"A year (or more) after this course is over, I want and hope that students will have seen value in what they learned and feel as though they built a strong foundation around conceptual understanding of the material and their ability to think critically and work with peers towards a common goal.”

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My Big Hairy Audacious Goal (BHAG) for the course is:

Learners will apply their prior knowledge and foundational algebra skills to quadratics functions/equations to gain a conceptual understanding of the properties and real-life applications of the content via collaboration, problem-solving, and critical thinking.

 

 

Foundational Knowledge

It is important that learners understand and remember the roles that x-intercepts/roots/zeros and the vertex play(s) in a quadratic function as well as the idea of real vs. imaginary roots. Learners should understand the roles these components play in a graph as well as in a real-life context.

It is important that learners in this course can relate the idea of transformations with graphs from function to function. Learners in this course should also be able to relate the algebraic concepts to their graphical representations.

 

Application Goals

Teaching mathematics in a lecture format is typical and has shown the be effective at times, but much of this unit will be in a blended learning setting where students are responsible for being the catalyst for their learning.

 

• Critical thinking

  • Learners will be expected to apply their procedural and instrumental understanding of quadratics to real-life scenarios.

  • Learners will make connections to their prior knowledge to generate hypothesis/conjectures and apply these to their assigned catapult project.

• Creative thinking

  • Learners will apply what they learned in the catapult project as well as their knowledge of quadratics to develop their own project related to quadratics.

  • The message of finding a project based around their interests will be emphasized.

• Practical thinking

  • Learners must think outside of the box and making observations based on their discovery activities to draw conclusions.

 

Students must gain the ability to find the important points of a quadratic equations, that is, the vertex and intercepts. Additionally, they should be able to graph a quadratic and justify transformations done to a graph.

 

Student will be assigned a catapult project where they will be expected to work with a group towards a common goal of landing a penny in a bucket. They will be expected to determine where to place their catapult based on the height of the bucket. Students will then be asked to create their own project based around quadratics. These will both be group projects where they will have to use their collaboration skills to work with a team.

 

Integration Goals

Mathematics is an extremely cumulative subject where learners are consistently expected to relate new concepts to their prior knowledge. It is expected that they are doing what they must do on their own time, particularly in an honors course, to ensure they have a strong foundation of past content. This is especially important in a learner-driven classroom.

• Graphing quadratics will be an extension from the previous unit which ended with absolute value functions. It is imperative that discussions occur in the class connecting the two concepts.

• Some students who have taken physics may relate the quadratic functions to studying projectile motions (this is typically any 11th grade students in the course).

• The student created group project should revolve around student interest. This will give students to opportunity to see relationships between the material and themselves as individuals.

 

Human Dimensions Goals

Student should see this as an opportunity to take ownership of their own learning and develop their ability to self-assess. They will be expected to persevere through some adversity, which is one of the most important skills that they can develop within this course.

 

The ability to collaborate with peers and work as a team towards a common goal will be a focus throughout this unit. Certain members of the groups will naturally take on different roles based on their skillsets. Engaging in an authentic learning community of this sort will allow students to continue to develop their communication skills to ensure they are working in an efficient manner.

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Caring Goals

Students will adopt the ability to truly take ownership of their learning and they will be the driving force behind what they obtain. This will give them more confidence moving forward when they are faced with a challenge to overcome.

They will also put value and trust in their peers, an important skill in any field. Generating a project collaboratively based around themselves, rather than one simply given by the teacher, will allow them develop skills that would not typically be used in a lecture format classroom.

 

“Learning-How-to-Learn” Goals

Although the subject of quadratics may be somewhat unfamiliar, the new mathematical skills the students are learning are based around prior knowledge. Productive struggle is one of the most pivotal components of learning, but uncomfortable for many. I would like students to feel okay with struggling at times and see the value in it. It is a natural reaction for students to raise their hand as soon as they are unsure about something, especially in an honors course, but true learning takes place when the students have to problem solve and think to get their answer.

When discussing test taking skills, we often discuss having a game plan for how to address a question. This idea of a “game plan” can and should be generalized to the learning process. When working through the catapult projects, students should identify what it is they are trying to achieve and work backwards to come up with a plan to get there.

 

References

 

Fink, L. Dee, PhD. A self-directed guide to designing courses for significant learning. N.p.: n.p., n.d. PDF.

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Harapnuik, D. (2015, August 15). Connecting the dots vs collecting the dots.

           Retrieved from https://www.youtube.com/watch?time_continue=16&v=85XpexQy68g