Aligning Outcomes, Assessment and Activities: Ensuring Student Success

Creating a significant learning environment requires educators to be mindful of many aspects and perspectives of content mastery. With Fink’s guide, it is best to use these multiple perspectives including application, integration, human dimension, caring, and learning how to learn.

As an educator, creating this guide supports students in successfully comprehending the content because it was created proactively with the “end in mind”, or with what many call backwards planning. Often times, backwards planning is something that is unfortunately overlooked in the classroom.

With Fink’s guide, I have curated an overview for a unit with my 7th grade math class. Ideally, I would create one of these guides for each unit my students are taught in both 6th and 7th grade. It would work nicely with the blended learning plan and provide a succinct location to embed links. This would be an excellent summer project for all educators in charge of their content.

Learning Environment & Situational Factors to Consider

1.  Specific Context of the Teaching/Learning Situation

How many students are in the class?  Is the course primary, secondary, undergraduate, or graduate level?  How long and frequent are the class meetings?  How will the course be delivered: live, online, blended, flipped or in a classroom or lab?  What physical elements of the learning environment will affect the class? What technology, networking and access issues will affect the class?

• Students: 57 students, 3 class periods
• Secondary level, 7^th grade
• 45-minute class periods Monday- Thursday, Friday’s classes are 33 minutes in the morning and 45 minutes in the afternoon.
• Delivery method: blended learning station rotation model with introductory problem-based unit lessons
• Each of the 3 classrooms are different (teachers are still rotating to the students per COVID protocol). 1 classroom is a lab and 2 are standard general education classrooms
• Several students will be virtual while most students will be in-person (due to COVID protocols)
• We have one-to-one Chromebooks with updated Wifi for in-person students. Virtual students will be connected to their personal Wifi Networks of varying strength and connectivity issues.

2.  General Context of the Learning Situation

What learning expectations are placed on this course or curriculum by: the school, district, university, college and/or department?  the profession?  society? 

• RenWeb communication of homework and grades with parents and students, in addition to Google Classroom for housing access to digital copies of all assignments.
• Grading criteria of A-D is required to be utilized for 9 weeks grading students
• 7^th Grade Math Diocese of Dallas Standards (They mirror the TEKS state standards for 7^th grade)

3.  Nature of the Subject

Is this subject primarily theoretical, practical, or a combination?  Is the subject primarily convergent or divergent?  Are there important changes or controversies occurring within the field?

• Subject (proportional reasoning) is both theoretical and practical.
• The topic is primarily convergent (connecting proportional reasoning to a multitude of real-world applications), but can also be seen as divergent because basic proportions understanding is necessary for extending the knowledge to all of the other applications.
• No true controversies, other than how to teach a new math concept (algorithm first, or connections to prior knowledge/ real-world application).

4.  Characteristics of the Learners

What is the life situation of the learners (e.g., socio-economic, cultural, personal, family, professional goals)?  What prior knowledge, experiences, and initial feelings do students usually have about this subject?  What are their learning goals and expectations?

• The school is in an affluent area in Dallas. A majority of the students are Anglo-American.
• Students should have learned about proportions in 6^th grade. They also should be familiar with using equivalent fractions and ratios from 5^th and 6^th grades. Students’ attitudes toward mathematics vary. The importance of a growth mindset has been emphasized in the classroom.
• Students are familiar with fractions, ratios and proportions from the year before. However, students may not have a deep understanding of conceptual foundational knowledge of fractions and ratios.
• Learning goals and expectations overview: understand and apply knowledge of ratios, rates and unit rates to proportional reasoning in real-world applications while connecting representations such as tables, graphs and equations to help solve proportions, percent proportions, and percent increase and decrease.
  • Current statement of inquiry that will drive the unit: The exploration of ratios, rates and unit rates and how they can be used in proportions to make sense of the world through multiple representations.
    • Expectation at the end: Students will create a presentation regarding a real-world application of proportional reasoning while using multiple representations to display the data.

5.  Characteristics of the Teacher

What beliefs and values does the teacher have about teaching and learning?  What is his/her attitude toward:  the subject? students? What level of knowledge or familiarity does s/he have with this subject?  What are his/her strengths in teaching? 

• Proportions can be a challenging topic because students often shy away from ratios and fractions due to a lack of conceptual understanding. However, students thoroughly enjoy making connections to real-life and sharing their creativity.
• I prefer to teach in a constructivist fashion in which students are allowed to explore with real-world and engaging problems. Activities and lessons that allow for real-world connections and deep understanding of concepts (such as hands on manipulatives) are used to support learning.
• This unit will be taught following a review of all operations with rational numbers, so an emphasis on the utility of proportional reasoning needs to be made. Almost all of what we learn following this unit will have some connections to proportional reasoning, so it will be necessary to create engaging, fun, and memorable connections to proportional reasoning.
• Students are frequently wary of proportions and fractions, so making this unit fun and engaging will provide a strong foundation from which their knowledge will extend. One of my strengths is how I understand the need for students to make connections to the real-world in order to see the usefulness of proportional reasoning. In order to get buy-in to the project, students will need to be engaged and challenged throughout the unit.

Questions for Formulating Significant Learning Goals

A year (or more) after this course is over, I want and hope that students will recognize the important, real-world purpose of proportionality and conceptually understand the importance of finding equivalent ratios to make sense of the world around them and use the knowledge to make informed decisions.

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

Learners will create and share a personal, real-world representation and presentation that explains a situation in which it would be helpful to use proportional reasoning.

Foundational Knowledge

• What key information (e.g., facts, terms, formulae, concepts, principles, relationships, etc.) is/are important for students to understand and remember in the future?

Standards:

• Proportionality. The student represents and solves problems involving proportional relationships.
• 7.5A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt
  • 7.5A.1 calculate unit rates from rates in mathematical and real-world problems 
  • 7.5A.2 determine the constant of proportionality (k = y/x) within mathematical and real-world problems 

• 7.5B represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b

• 7.5C solve problems involving ratios, rates, and percent, including multi-step problems involving percent increase and percent decrease, and financial literacy problems 

• What key ideas (or perspectives) are important for students to understand in this course?
  • Understand the importance of ratios and what they represent.
  • Comprehend the difference and similarities between fractions, ratios, rates and unit rates.
  • Understand what equal means and what it means to have equivalent ratios.
  • Make the connection between simplifying fractions and finding equivalent ratios.
  • Recognize the purpose and develop a conceptual understanding of cross-multiplying or finding a scale factor.
  • There are multiple ways to represent the same data. There are varying benefits to using a graph, table, and equation.
  • Comprehend the connection between d=rt and extend the knowledge to understand y=mx +b

Application Goals

•   What kinds of thinking are important for students to learn?
  • Critical thinking, in which students analyze and evaluate
    • Students will need to interpret and analyze data represented in equations, tables, and graphs, and evaluate real-world situations to connect how proportional reasoning is valuable.
  • Creative thinking, in which students imagine and create
    • Students will be required to create a real-world problem and apply existing knowledge to create equations, tables and graphs that represent the situation.
  • Practical thinking, in which students solve problems and make decisions
    • Students will need to apply knowledge of proportional reasoning to real-world situations to make useful decisions by applying and extending their knowledge to identify how proportional reasoning is valuable.
• What important skills do students need to gain?
  • Students should finish the unit with evaluative and analyzing skills, as well as proportional reasoning, which will come in hand throughout their rest of their years whether they are shopping or finding a best deal, and continuing their education as mathematicians.
• Do students need to learn how to manage complex projects?
  • Yes, students will certainly need to learn how to manage their project. Throughout the process, I will be scaffolding and providing guidance through SMART goals and checkpoints.

Integration Goals

• What connections (similarities and interactions) should students recognize and make…:
  • Among ideas within this course?
    • Students should see the relationship between proportional relationships and tables, equations, and graphs. Students should also be able to understand the relationship between unit rates, rates, and ratios and how finding equivalent ratios is necessary in order to identify proportional relationships.
  • Among the information, ideas, and perspectives in this course and those in other courses or areas?
    • Proportions will follow students throughout the rest of the career with Algebra. Students will need to understand ratios and proportions in order to extend their knowledge in further courses. Students additionally will need to develop communication skills and become comfortable presenting their ideas to others.
  • Among material in this course and the students’ own personal, social, and/or work life?
    • Proportional reasoning and identifying unit rates will be helpful in the frequent decisions students make in stores while buying or selling items. Students also will see the connection between displaying and manipulating data to benefit the seller or the buyer.

Human Dimensions Goals

•  What could or should students learn about themselves?
  • Students will be able to learn about choices they make and how what they purchase can affect their finances. Students also can use proportions to make predictions about spending using various representations.
• What could or should students learn about understanding others and/or interacting with them?
  • Students will learn about how to be better stewards of their personal and family’s resources and will be able to discuss reasons to save money and be mindful of their spending habits.

Caring Goals

• What changes/values do you hope students will adopt?
  • Feelings: I hope that students develop an understanding and comfort regarding mathematics and how math is meant to make sense.
  • Interests: I hope students develop an interest in finding good deals and develop ethical and moral reasons to be mindful with their money.
  • Values: I hope students will find value in using proportional reasoning in the real world and find value in how mathematics can be useful to them in frequent real-world situations.

“Learning-How-to-Learn” Goals

What would you like for students to learn about?

• How to be good students in a course like this?
  • I would like for students to learn how to manage their time best through organizational skills with their agenda books, as well as learn how to use math to help them make informed decisions.
• How to learn about this particular subject?
  • I would like for students to learn that math should be used to make sense of the world around them.
• How to become a self-directed learner of this subject, i.e., having a learning agenda of what they need/want to learn, and a plan for learning it?
  • I would like for students to learn how to independently set SMART goals to help them accomplish larger goals.

 3 Column Table 

BHAG (Big Hairy Audacious Goal) – Overarching Course Goal

Learners will create and share a personal, real-world representation and presentation that explains a situation in which it would be helpful to use proportional reasoning.

Learning Goals	Learning Activities	Assessment Activities
Building a Foundation: Learners will understand the importance of ratios and what they represent. Learners will comprehend the difference and similarities between fractions, ratios, rates and unit rates. Learners will understand what equal means and what it means to have equivalent ratios. Learners will make the connection between simplifying fractions and finding equivalent ratios.	Station-rotation classroom notes and practice assignments. Guided practice and note taking during stations regarding ratios, rates and unit rates, as well as hands-on activities and models displaying ratios, rates and unit rates, as well as equivalent ratios.	A variety of formative/ summative assessments (both for grading and providing student feedback), Kahoots!, Quizlet Live! Formative feedback during station rotation teacher station.
Applying Knowledge: Students will need to interpret and analyze data represented in equations, tables, and graphs, and evaluate real-world situations to connect how proportional reasoning is valuable. Students will be required to create a real-world problem and apply existing knowledge to create equations, tables and graphs that represent the situation. Students will need to apply knowledge of proportional reasoning to real-world situations to make useful decisions by applying and extending how to identify how proportional reasoning is valuable.	Discussion Creation of equations, tables and graphs with real-world problem-based activities. Better-buy activity and discussions	Assessment on graphing, creating tables and equations. Assessment of applied knowledge to similar situations.
Integration: Learners should see the relationship between proportional relationships and tables, equations, and graphs.  Learners should be able to understand the relationship between unit rates, and ratios and how finding equivalent ratios is necessary in order to identify proportional relationships.	Discussion Distance Project  Practice assignments and stations during station-rotation time.	Assessment on distance project. Formative assessment and feedback through discussions and practice assignments.
Human Dimension: Students will be able to learn about choices they make and how what they purchase can affect their finances.  Learners can use proportions to make predictions about spending using various representations. Learners will discover how to be better stewards of their personal and familial resources and will be able to discuss reasons to save money and be mindful of their spending habits.	Conversations/ Discussion in Class Budgeting Activity Discussion/ interview with family.	Reflection on discussions and conversations with classmates. Budgeting Assignment Worksheets/ budgeting quiz
Learning How to Learn: Learners will learn how to manage their time best through organizational skills. Learners will learn how to use math to make informed budgeting decisions. Learners will learn how math should be used to make sense of the world around them. Learners will learn how to independently set SMART goals to help them accomplish larger goals.	Using student agendas Budgeting worksheets Feedback/ discussion from classmates regarding presentation Project planning pages	Check worksheets Final project summative assessment (graded with rubric)

References

Fink, L.D. (2003) A Self-Directed Guide to Designing Courses for Significant Learning. San Francisco: Jossey-Bass.