3 Column Table
I used Fink’s, Self-Directed Guide to Designing Courses for Significant Learning, to create an overview of a Multiplication Unit in a 3rd Grade Math Course that students can complete in a significant learning environment (2003).
BHAG (Big Hairy Audacious Goal) – Overarching Course Goal
For students to feel confident in using various multiplication strategies to make accurate calculations and be able to relate this to real life problems, or situations while working together in engaging, fun, and collaborative ways.
Learners will use the following 3 column table to align learning goals, activities, and assessments to learning different multiplication strategies used for calculations and problem solving. Most importantly, this table lines up with my innovation plan and supports my ideas of a blended learning environment that incorporates a flex model approach using an LMS, project based learning, and small group instruction.
How the course outcomes and 3 Column table will affect my Innovation Plan:
Flexible Learning Paths – Students will learn at their own pace with online lessons, projects, and teacher support.
Teach Integration with Schoology – The course outcomes and 3 Column table will connect a digital learning management system, like Schoology, to projects that students work on together, and teacher instruction is in a small group to ensure that all parts are working together in the classroom and providing a blended learning with a flex model approach.
Focus on Project-based Learning – Students will collaborate to work on projects that are a representation of real world experiences, and how it is used on a day to day basis.
Personalized Support: Students will have regular check-ins with the teacher in a small group setting, and the outcomes will drive the learning, which allows the teacher to give extra help to students on a personal needs basis.
| Learning Goals | Learning Activities | Assessment Activities |
| Foundational Knowledge: Students will learn, understand, and use multiplication strategies, such as, repeated addition, equal-sized groups, arrays, area models, skip counting, and equal jumps on a number line. | Video lessons of different ways to multiply, and interactive activities with multiplication on Schoology. Small group discussion and practice using manipulatives, like counters, number blocks, and square tiles. | Create LMS quizzes to assess understanding of different ways to multiply, using various strategies. Group activities with skip counting, and using arrays to multiply to find a product. |
| Application: Students will solve one and two step multiplication word problems, and apply the appropriate strategy that they used to find the solution. | Small group problem solving, and focusing on real world problems involving multiplication. Collaborative projects that solve real life math problems, like using arrays to create a map, area model to design a garden, or calculating items in a grocery store. | Assessment of multiplication word problems through a created LMS quiz, particular to one and two steps. Group reflection of multiplication strategies used to solve real world word problems. |
| Integration: Students will create a project to demonstrate their understanding of solving one and two step multiplication word problems using real world scenarios, and make connections to other areas of math, such as addition, or division. | Project Based Learning: Students can design a store where they calculate how many items they have, and the total cost of the items using multiplication, or repeated addition. They can connect multiplication with division to share items among a group of people. Students can research prices and quantities online, and collaborate their ideas with others using an LMS, such as Schoology. | Rubric based assessment of the presentation of their store project. Evaluate how well multiplication strategies were applied throughout the project. |
| Human Dimensions: Students will collaborate with peers in a small group setting to share ideas of how they used the different strategies to multiply. | Students will have a small group rotation with the teacher as a guide, to continue to practice and reinforce multiplication strategies for calculations, and problem solving. Students can mentor, or coach one another so that they can show their level of understanding by helping someone else. | Observations are made by the teacher, to see how students are sharing and collaborating, especially in a small group setting. Students can give feedback on teamwork and communication during collaborative projects. |
| Caring: Students will use Schoology to track learning, and they can use this LMS to complete their assignments. They will develop an appreciation for using math in their daily lives, and build their confidence with their newly gained skills. | Upload assignments involving different strategies for multiplication, and problem solving. Use Schoology as a discussion board to talk about challenges, and solutions with one another in a non formal way. Students can even discuss math careers and how math is used in them. | Use LMS to complete handouts, and digital work related to multiplication calculations, and problem solving. Students self assess, through digital reflection forms, or polls in Schoology. Students can also use discussion boards to talk about the importance of using multiplication. |
| Learning How to Learn: Students will identify multiplication strategies, and learn how to apply them to multi step problem solving that involves other operations, such as, division, addition, or subtraction. They can take ownership of their own progress, and growth. | Students will learn how to use multiplication charts, flash cards, songs, apps, and skip counting for extra practice on their own. Students will set personal goals that are related to multiplication, and problem solving, and track their own progress. | Students can have conferences with the teacher to discuss their level of understanding different multiplication strategies, and how to apply critical thinking with real world problem solving. |
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 lab, or classroom? What physical elements of the learning environment will affect the class? What technology, networking and access issues will affect the class?
This is a 3rd Grade Math Class in an elementary school setting. There are two classes of about 20 students currently in each classroom. Each class meets for math everyday for about an hour and a half for each block of time. This course is delivered in a blended learning environment, where students and teachers are face to face, yet students also have a flex model approach, and can rotate to small group instruction with the teacher, and do project based learning in collaborative groups. These students can move around the classroom freely, and they each have a one to one device initiative, where they can log in to Schoology to access their Math course and assignments.
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?
This is a 3rd grade class that focuses on foundational learning and skills, and this is an introductory lesson to using different multiplication strategies, using a hands on approach, with some digital tools, such as Schoology, an LMS that can be used to incorporate videos, assignments, and quizzes. Students will do calculations, then move into problem solving skills using multiplication in a real world setting, and approach. Students will also meet in small groups with the teacher, and work on projects based on what they are learning with their peers.
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?
This 3rd grade math class will be a combination of theoretical and practical learning. Theoretical because it is based on learning and understanding of multiplication rules, using practical skills to make calculations, and solving real world problems. It is an example of practical learning because students will use manipulatives, and have a hands on approach to learning these different multiplication strategies. Since this is happening in a learning environment that is blended, it is both convergent and divergent. It is convergent because the students are using multiplication skills to solve math equations, and it is divergent because students are using creative problem solving, and project based learning to show that they can solve real world multiplication problems in many different ways. Learning how to multiple is pretty stable, and there are not very many changes to it. However, there are different ways to facilitate, or teach multiplication to students, such as using a flex model approach to blended learning, and using a digital platform, like Schoology, or project based learning in groups.
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?
In each math class, learners come from diverse home environments, where some have strong family support, and others are limited due to various constraints, such as economic factors, and educational resources. Students should have foundational skills using addition and subtraction from 2nd grade. Some students have a small amount of exposure to multiplication, or learning repeated addition, and can relate it to multiplication. Some may need additional support using Schoology, or working on projects with their peers, or in groups. All of this can create mixed feelings of excitement and frustration, since they are now learning multiplication, using an LMS, and learning to work on projects more freely and independently without teacher supervision, rather than having a facilitator to guide them. The end goal is for these 3rd graders to master foundational math skills using many different multiplication strategies, then move into more advanced problem solving, and critical thinking skills. Students are expected to learn in a blended learning environment with both a traditional setting and using digital tools to become independent learners and meet their learning goals.
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?
The teacher needs to believe in and support student centered learning, and have students take an active role in their own learning journey, or education. The teacher should foster a growth mindset that encourages students to view a challenge as an opportunity to learn, and grow. The teacher needs to be open to using digital tools, and technology to create an engaging, fun, and interactive approach to learning. In essence, the teacher guides the students to have a personalized learning journey. The teacher should have passion to teach math concepts such as multiplying in different ways, and show students creative and exciting strategies to use to make calculations accurately. The teacher’s attitude will be a reflection in the teaching methods that are used, and be impactful when presenting the content that students need to learn. The teacher needs to know that the students are capable, and the students should be encouraged to ask questions, openly explore, take risks, and problem solve. The teacher should strive to be positive, and supportive to build strong relationships and connections with students that come from various backgrounds, and have personal needs. The teacher needs to understand multiplication strategies and be able to show students how to use the different strategies, or approaches. Students need guidance on misconceptions, and differentiation of the concepts. The teacher needs to be strong at integrating technology, incorporating project based learning, and providing guidance in a small group. Collaboration and positivity are a must have in this learning environment, and supporting students in their independence, as well as their ability to work with their peers is a necessity.
Questions for Formulating Significant Learning Goals
“A year (or more) after this course is over, I want and hope that students will ..”
Understand and apply different multiplication strategies using real world, and complex problem solving. Apply multiplication to multi digits, and relating multiplication to division. Recognize the importance of multiplication and using it in everyday life, along with algebraic reasoning. Build flexibility and know when to apply certain strategies, and know how to use the best methods on their own. Gaining confidence to multiply with larger numbers, and even how to apply it to fractions in 4th grade math. Overall, I want the students to be able to deepen their understanding of critical thinking and problem solving.
My Big Hairy Audacious Goal (BHAG) for the course is: For students to gain knowledge and confidence in using various multiplication concepts, and strategies, then relating it to real world situations, in 4th grade and beyond, with a more complex, and deeper understanding of the foundational skills, and tools to relate to algebraic reasoning, and critical thinking.
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?
- Multiplication Facts: 0 through 12, knowing basic facts with fluency and automaticity
- Properties of Multiplication: Commutative Property, Associative Property, Identity Property, Zero Property
- Terms: Factor, Product, Array
- Multiplication Formula: factor X factor = product Area Formula: Length X Width = Area
- Concepts: Repeated Addition, Arrays, Distributive Property, Inverse Relationship with Division
- Multiplication principles remain the same, whether multiplying small or large numbers.
- Multiplication is used in everyday life, such as, solving word problems, calculating totals, and measuring area.
- Relationships: Multiplication connects to addition, Multiplication connects to division, Multiplication connects to geometry
- What key ideas (or perspectives) are important for students to understand in this course?
Multiplication is used as a tool to solve real world problems, combining equal groups. There are different ways to multiply and approach word problems. Being flexible is a valuable key to understanding. Choosing the best strategy can depend on the type of problem it is. Multiplication relates to addition, division, fractions, and geometry. It is a connection to other math operations. Multiplication relates to real world problems and connecting to how many items are needed, calculating the costs, or finding the area. Multiplication involves practice and determination. It requires a growth mindset and a resilient attitude. It is about making mistakes, and learning from them. Math is about being persistent, and being willing to improve over time. It is about working with others to solve problems, and foster a deeper understanding that builds on foundational skills.
Application Goals
- What kinds of thinking are important for students to learn?
- Critical thinking, in which students analyze and evaluate
- Creative thinking, in which students imagine and create
- Practical thinking, in which students solve problems and make decisions
Students should be able to analyze and evaluate the best multiplication strategies, such as, comparing when to use arrays versus repeated addition to get the quickest answer. Students should be able to use critical thinking to break down word problems into parts to have better understanding, and they should be able to explain why they chose a particular strategy, or solution. Students should be able to create their own word problems and use visual, and manipulatives to represent their multiplication strategies. They can even create a multiplication board game, or use it in fun, and unique ways to show their understanding of the concept. They can create a project that uses multiplication in creating a special event, such as a birthday party, or using multiplication skills at a grocery store.
- What important skills do students need to gain?
Students need to be able to recognize multiplication in everyday life, such as gardening, cooking, and budgeting. Students should also learn how to check their own work, and make sure that they are accurate.
- Do students need to learn how to manage complex projects? Yes. Students need to learn how to manage complex projects so that they can use it to make connections to other subjects. Integrating with projects allows them to build more skills that will be useful later in life, such as planning, organizing, management, team work, and communication.
Integration Goals
- What connections (similarities and interactions) should students recognize and make…:
- Among ideas within this course?
Students need to be able to choose the right strategy to use for themselves, and which way to solve the problem would be the most efficient to use. They need to recognize that the strategies interconnect with one another. For instance, arrays can represent repeated addition, and can help them build on their concepts in a stronger way.
- Among the information, ideas, and perspectives in this course and those in other courses or areas? Students should be able to connect multiplication to repeated addition, division, geometry, fractions, as well as, science, technology, and art.
- Among material in this course and the students’ own personal, social, and/or work life? Students can relate it to their personal life. For example, in areas like cooking, multiplication is used for adjusting recipes, like doubling or halving ingredients. And, in their social life, students can relate multiplication to parties or events, and figure out how many items to bring, or how much food, or snacks are needed. They can relate it to their future careers by estimating costs, scheduling hours, or managing inventory.
Human Dimensions Goals
- What could or should students learn about themselves? Students will learn which approach to multiplication suits them best, like using visuals, hands on activities, or listening. They might find that they love arrays, or skip counting. They may learn that they can do hard things and overcome their challenges. They can learn to set goals, and track their progress.
- What could or should students learn about understanding others and/or interacting with them? Students can learn to problem solve with others, and practice their concepts in creative ways that relate to real world scenarios. They will learn to help someone who is struggling, or allow themselves room to not know something the first time around.
Caring Goals
- What changes/values do you hope students will adopt?
Feelings? Students can gain confidence, and curiosity with math concepts and problem solving strategies. They can find it fun, and engaging to learn multiplication skills.
Interests? Students can work on projects, and collaborate with others in a group setting, and learn to apply it to everyday life. Learning the different strategies opens them up to trying new things.
Values? Students can try hard, and not give up. Plus, learn to help themselves or someone else in their struggles, and value other people’s ideas and feelings.
“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 ask questions and join in the class discussions for a deeper understanding. Practice at home to reinforce what they have learned. Engage in activities to make multiplication fun, and engaging. Seek help when needed, and reflect on what they have learned with multiplication.
- How to learn about this particular subject? Students can play educational games, and use digital apps that allow for extended practice with the multiplication strategies.
- 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? Students can set learning goals, and have a learning plan. Ask for feedback, and check for their own understanding, or reflection.
References
Fink, L. D. (2003). Self-directed guide to designing courses for significant learning. Jossey-Bass.
Jackie Bittner M.Ed. 