The purpose of this curriculum is to develop sixth grade students’ abstract thinking skills and the use of mathematical modeling to solve problems presented to them. In the unit credit, students learn, develop, apply, and compete as they go along, allowing them to strengthen their understanding of mathematical models and abstract solutions. Each lesson is based on the use of the appropriate CCSS standard, meeting high academic reliability and planning accuracy.
Curriculum Map
The Mathematics Abstract Skills Development Curriculum Map provides an overview of a single unit instructional week that consistently develops in students the critical skills associated with using mathematics in life lessons. The structure of the unit week is seven lessons, in the first six of which students consistently recall basic arithmetic, geometric, and statistical counting skills and then apply what they have learned to solve practical problems. The last lesson in the Unit is a competitive, team-based game in which students summarize and apply what they have learned and develop soft communication skills such as teamwork, presentation, and project defense.
Outline of the Curriculum: Goal and Objectives
The goal of the curriculum is for students to practice key math skills that are applicable in solving life problems, as well as to develop communication competencies related to teamwork. Since this is a broad goal, it needs to be fragmented into objectives that must be met in order to achieve the goal. Specifically, this curriculum had the following objectives:
- To create optimal conditions for practicing key abstract skills in mathematics.
- To develop students’ skills in defending their project against criticism and defending their position and responding appropriately to criticism.
- To develop students’ ability to take responsibility for the entire team during the presentation of the solution (Martin, 2020).
- To examine students’ special learning needs and adapt the curriculum for them as needed (Kaur, 2021).
- To examine the segmentation of the class by mathematics proficiency to ensure sufficient division into nearly equivalent teams.
- To prepare printable materials (cards, manuals) to be used by the student in each lesson.
Scope and Sequence
The scope of the Mathematics Abstract Skills Development Unit is expected to be one week in which students repeat or learn current information in the context of the lesson. The philosophy of this Unit is based on a deductive approach in which students are first introduced to some theoretical foundations of arithmetic, statistics, and geometry, and in the last, most challenging lesson, implement what they learn in private practice, a competitive game between teams. This approach is entirely consistent with standard academic practice, in which students first go through (recall, repeat) the more straightforward knowledge and concepts, then work through them in greater complexity (Matthews, 2019). In other words, all lessons in this Unit are found to be dependent and connected to each other by a common idea that the teacher communicates to the students in the first lesson.
Assessment of Needs
The Unit Needs Assessment responds to a systematic process of checking the alignment between current skills and students and the outcomes they must possess in order to complete the Unit successfully. The core of the needs assessment in this Unit is the first six lessons that invite students to practice their own knowledge and competencies before proceeding to the summative lesson of the week. This ensures that students are sure to have fresh memories and practice with the specific tasks they will encounter in Lesson #7. Outputs from each lesson (formative assessments) are also used for a needs assessment to assess how effectively each student has learned the material before proceeding to the next task. If it becomes clear from the formative assessments that some students do not have enough competence to move to the next level, they will be asked to practice after lessons or do extra homework to practice the skills.
Assessment Plan
The Unit provides several strategies for both formative and summative assessment of student knowledge and skills. Formative assessments are designed to assess the knowledge gained so far, that is, during a particular lesson, whereas summative assessments are used as the completion of a Unit in order to examine the consolidation of knowledge (Prescott, 2022). Formative assessments in this Unit include task cards that each student completes individually during the lesson and turns in for review, self-assessment cards where students are asked to rate their understanding of the material on a smiley-face scale, and a minigame in which students have to explain a specific topic to a five-year-old child. For example, the teacher might ask a student to explain how to use a pie chart to an abstract five-year-old so that the teacher can assess the student’s level of understanding of the topic. After each lecture lesson (#1, #3, #5), students are asked to complete a homework assignment that evaluates the knowledge gained in the lesson-the deadline for completing the homework is the period until the next lesson. Finally, an open-ended discussion in practice lessons (#2, #4, #6) about what ideas they have for solving a particular problem is also used as a formative assessment. For example, if the task involves determining from a bar graph which of the months in the state has the most rainfall, the teacher initially addresses the entire class to hear strategies and solution ideas. The teacher mainly focuses on students who are inactive in the discussion and prefer to remain silent. As a summative assessment, the last lesson in the Unit is used, during which students are divided into teams of roughly 3-4 individuals per team so that each team has both an underachieving and an overachieving student (Garside, 2020). Students complete a competitive game assignment that results in a ranking of teams based on the number of points scored and the final grade for the Unit. Scores for the presentation are given both by the teacher, who assesses not only the mechanism for solving a particular problem but also the soft skills of the student and by the students. In particular, each student from groups different from the group of the performing student must evaluate their peer on the criteria of the attractiveness of the solution presentation, simplicity, and general understanding, as well as the ability to answer questions. Based on the results of all evaluations, the teacher decides which team wins; it receives rewards, such as an exemption from homework and an A grade.
References
CCSSI. (2020). Grade 6 » The number system. CCSSI. Web.
Garside, T. (2020). Differentiation — why should you do it more? 4 ways to make sure no student gets left behind. Language Point. Web.
Kaur, N. (2021). Curriculum adaptation for the learning disabled [PDF document]. Web.
Martin, A. (2020). Team-building activities for middle school. Teach Hub. Web.
Matthews, E. (2019). How to develop a curriculum as a new teacher. Class Craft. Web.
Prescott, J. (2022). Formative vs. summative assessment in the classroom. HMH. Web.