Place Value, Fractions, and Algebra: Improving Content Learning through the Practice Standards

Strategies

This curriculum unit will be completed in three to four weeks, depending on the school schedule of regular, collaboration or block scheduling of classes, within an 18-week semester schedule at WCO. The course that is most suitable for this unit is CCIM-I, although it can be used in Common Core Math 8 (CCM-8), Summer Bridge Programs for incoming ninth graders, and in Common Core Traditional Algebra I. I will be teaching this curriculum unit to ninth and tenth grade students in the CCIM-I course in a comprehensive high school setting. The class periods range from 40 to 55 minutes each day and this course will be one of at least four academic courses students will take within a complete school day. Many of the lessons in this unit will incorporate common teaching strategies such as whole-class discussions, graphic organizers and composition books to maintain notes on content knowledge and skills, think-pair-share, collaborative group work, and individual tasks. These teaching strategies will help students be engaged in lessons and activities that are guided through the FAL process and the implementation of the 5 Practices Model ⁵ within the FAL process.

Formative Assessment Lesson

There are many types of skills used to acquire knowledge that students will need to focus on for 21 ^st century college and career readiness and navigate through life, one of which is critical thinking skills. This entails interpreting information and drawing conclusions as well as seeking relationships and patterns ⁶. The sequence of lessons in the FAL will address these skills, introduce students to a new curriculum through the CCSS-M, including the application of the CCSS-MP that require students to expand on their creativity, take ownership of their own thinking and learning process both inside and outside of the classroom. Students will become an integral part of small collaborative groups and whole class discussions to defend and support their thinking process. The FAL process will encourage students to be active participants in their learning and actively engage in the process of solving problems to produce and make sense of solutions to problems.

The FAL process will guide students through the mathematical thinking and learning needed for success in this curriculum unit. Research has shown that effective teaching strategies that assess students and require they apply their prior learning assist teachers in the process of adapting their teaching to the needs of their students ⁷. There are also some instructional strategies that are used in the FAL process that help improve instruction: clarify learning intentions for student success, facilitate effective whole-class discussions and collaborative learning tasks, provide feedback to move student learning forward, encourage students to be instructional resources for each other, and encourage students to take ownership of their own learning ⁸

The FAL process is used to measure student learning and as a means to re-engage students in their learning process. Students take ownership of their learning through assignments, tasks, activities, and assessments. It is an important skill for students to determine mistakes in their own thought process and have the resiliency to fix those mistakes using prior knowledge and new knowledge. Instructors are able to use results from class discussions, activities and assessments to improve their teaching strategies and re-engage students by addressing common misunderstandings.

When viewed as a process, the FAL is a structure that lends itself to a gradual change leading to a particular result, a series of actions or operations leading to an end result, and the opportunity to receive information in order to generate an action or response. Successful implementation of the FAL process will take time, energy, planning and a deep understanding of student needs for successful implementation, all the while being student-centered in nature. The FAL process allows for meeting CCSS-M and promote the CCSS-MP throughout each step of the process. The result will be gradual changes in the way students think. It will encourage students to take actions based on the integration of their prior knowledge while receiving new knowledge, and allow them the opportunity to respond and take action leading to solutions.

A pre-assessment task is provided to each student to complete individually prior to the start of the FAL. This individual task is typically administered the last 15 minutes of a class period at least a day or two before the lesson is to be taught. This task is designed to reveal current understandings and misunderstandings of each student that will need to be addressed at the start of and throughout the lesson. The instructor must collect and review student work on the assessment task to create a list or chart of questions addressing the most common student difficulties and misunderstandings. This list or chart becomes a tool for instructors to prepare for whole-class discussions using the results from individual pre-assessment tasks. Whole-class discussions occur at the start of the first day the FAL is to be implemented. Research has shown that classroom discussions led by instructors are, "…one of the most universal instructional practices." ⁹ Instructors will address the common difficulties and misunderstandings in the form of questions or prompts within short tasks. "Questions solicit both knowledge and processing of knowledge at a designated cognitive level. Further, the effective question-answer exchange [will] …prompt students to provide answers that are either more correct, more complete, or at the desired cognitive level." ¹⁰Students will be given processing, or wait time to develop a response and then answer questions to improve their knowledge and contribute to whole-class understanding of a concept or skill. The purpose of this wait time is to provide students with time to develop longer responses and answer questions with confidence while teachers have the time to ask fewer probing questions so they can develop more thoughtful responses to students ¹¹.

Students will then transition into cooperative learning groups, also referred to as collaborative groups, for further discussions and work collaboratively to discuss and complete a task or activity to further address the common issues and misunderstandings from the individual tasks. "Sensible, sense-making mathematics makes extensive use of high-quality instructional and assessment tasks to introduce, develop, reinforce, connect, apply, and assess understanding of key mathematical concepts." ¹² Instructors should explicitly state the specific mathematical goals of the lessons and task so students can remain accountable for their mathematical learning and remain engaged in the lesson ¹³. Specifying explicit learning goals lends itself to evidence of student learning ¹⁴. The CCSS-MP are embedded throughout the collaborative group discussions and activities to promote student engagement and accountability. The activities within the collaborative groups range from simple tasks where students are completing skill based activities to more complex tasks where students will need to organize manipulatives in order to make sense of a situation, often given in a word problem scenario. During the collaborative group time, the instructor is tasked with implementing the 5 Practices Model ¹⁵ to identify and monitor student thinking throughout activities to select student work that will engage students in sharing their thought process and new knowledge that connects to the key mathematical ideas from the task. Instructors may find it useful to create and complete a chart ¹⁶ to monitor students' work on a specific task related to the strategies students use to complete their task or activity.

To bring the FAL to a close, there is a whole-class discussion to debrief on the task in which the instructor starts the discussion by helping students draw connections between their approaches to the task in relation to other students. This is where the chart is useful to begin calling upon students to present their findings and solutions to the task. The instructor also revisits the common difficulties and misunderstanding to the whole class in the form of questions. Students are given wait time to process and answer the questions with their new knowledge and better understanding about mathematics. The hope is students will improve their solutions on the post-assessment task with knowledge acquired through collaborative discussions and completing the tasks as well as keeping common misunderstandings in mind while processing through the collaborative task.