Midterm Module 1 PDF

MODULE: (Midterm) by: JONEL C. MURILLO, PhD TEACHER EDUCATION PROGRAM M119N: ASSESSMENT AND EVALUATION IN MATHEMATICS First Semester of A.Y. 2024 – 2025 Rationale This course is designed to provide students an in-depth knowledge and unders...

MODULE: (Midterm) by: JONEL C. MURILLO, PhD TEACHER EDUCATION PROGRAM M119N: ASSESSMENT AND EVALUATION IN MATHEMATICS First Semester of A.Y. 2024 – 2025 Rationale This course is designed to provide students an in-depth knowledge and understanding of the principles of valid and useful assessment and evaluation practices and their role in the educative process. The course gives emphasis on the use and development of modified traditional type of assessment, authentic and alternative assessment strategies to gauge the extent of learning in Mathematics. Moreover, it discusses issues and trends in assessment in mathematics teaching. As a requirement, the students are to construct test types aligned with the competencies and performance standards of K to 12 as well as construct evaluation tools for performance-based assessment. Specific Learning Outcomes After learning this module, you should be able to: 1. articulate performance standards into competencies 2. articulate competencies into learning targets 3. identify various authentic assessment methods in Mathematics education 4. select appropriate authentic assessment method that can be utilized in Mathematics teaching and learning 5. design authentic assessment method that integrates other discipline (Sciences, Social Studies, etc.) in Mathematics project Activating Content UNIT 3 Title: Performance Standards, Competencies, and Learning Targets in Mathematics (by Realiza and Garcia) Topic 1: Performance Standards, Competencies, and Objectives Defining Performance Standards, Competencies, and Objectives Performance Standards - Performance standards are predefined criteria or benchmarks used to assess how well individuals or entities (such as students, schools, or teachers) have met specific educational or performance-related goals or expectations. Performance standards provide a clear and objective basis for evaluating performance and determining whether established goals have been achieved. In education, performance standards are often associated with assessments and evaluations (ProctorEdu, 2020). Competency - A general statement that describes the desired knowledge, skills, and behaviors of a student graduating from a program (or completing a course). Competencies commonly define the applied skills and knowledge that enable people to perform successfully in professional, educational, and other life contexts (Gosselin, 2017). Objectives - A learning objective is student-centric; it states what the student will learn and be able to accomplish by the end of instruction. It describes a specific behavior which will lead to the desired goal(John Hopkins University, 2024). ABCD of the Statement of Objectives The ABCD method of writing statements of objectives provides a clear and structured framework for effective goal-setting. Each letter in ABCD represents a different component: A for Audience, B for Behavior, C for Condition, and D for Degree. By identifying the target audience, specifying the desired behavior or action, describing the conditions under which it should be performed, and defining the level of proficiency or mastery to be achieved, the ABCD method ensures that objectives are specific, measurable, and focused. This framework facilitates the evaluation of objectives and promotes clarity, measurability, and alignment with desired outcomes. The ABCD method of writing objectives can be aligned with Bloom's Taxonomy to create objectives that encompass different levels of cognitive complexity. Here's how the components of ABCD can be related to Bloom's Taxonomy: 1. Audience (A) and Behavior (B): The Audience component of ABCD focuses on identifying the target audience for the objective, while the Behavior component describes the specific behavior or action the learners should be able to demonstrate. These components align with the lower levels of Bloom's Taxonomy, such as Remembering and Understanding, where learners acquire and recall information. 2. Condition (C): The Condition component of ABCD defines the circumstances or conditions under which the behavior should be performed. This component can align with higher levels of Bloom's Taxonomy, such as Applying, Analyzing, and Evaluating, where learners apply knowledge, analyze information, and make judgments. 3. Degree (D): The Degree component of ABCD specifies the level of proficiency or mastery that learners should achieve. This component aligns with the highest level of Bloom's Taxonomy, Creating, where learners demonstrate their ability to generate new ideas, products, or solutions. Examples of Writing an Objective in Mathematics using the ABCD Format Example 1 Objective: "Students in a 7th-grade math class will solve 20 addition and subtraction problems given a set of problems with at least 90% accuracy." Audience: Students in a 7th-grade math class Behavior: will solve Condition: given a set of 20 addition and subtraction problems Degree: with at least 90% accuracy. Example 2 Objective: "High school algebra students will graph a quadratic equation given the equation correctly on a coordinate plane." Audience: High school algebra students Behavior: will graph Condition: given a quadratic equation Degree: correctly on a coordinate plane. Example 3 Objective: "College calculus students will differentiate five functions given the functions with at least 80% accuracy in their calculations." Audience: College calculus students Behavior: will differentiate Condition: given a set of five functions Degree: with at least 80% accuracy in their calculations. TOPIC 2: Articulation of Performance Standards into Competencies Why Articulate Performance Standards into Competencies? The articulation of performance standards into competencies is a critical aspect of teaching mathematics, as it provides a structured approach to ensure that students not only acquire knowledge but also develop the skills necessary to apply that knowledge effectively. This comprehensive discussion will explore the significance of this articulation, the processes involved, and its implications for teaching and assessment in mathematics education. 1. Clarity and Focus: Breaking down broad standards into smaller, more manageable competencies helps teachers and students understand the specific goals of instruction (Wiggins & McTighe, 2005). 2. Alignment with Instruction: Competencies can be directly aligned with instructional activities and assessments, ensuring that students are learning what they need to know to meet the standards (Grant & Grant, 2010). 3. Measurable Outcomes: Competencies can be assessed more effectively than standards, as they provide specific criteria for evaluation (Marzano, 2006). 4. Individualized Learning: By breaking down standards into competencies, teachers can tailor instruction to meet the individual needs of students (Tomlinson, 2000). Steps for Articulation: a. Analyze Performance Standards: Carefully examine the performance standards to identify the key knowledge, skills, and abilities required. This involves breaking down the standards into their constituent parts and understanding the underlying concepts and processes (Wiggins & McTighe, 2005). b. Identify Competencies: Break down the performance standards into smaller, more specific competencies that address the required knowledge, skills, and abilities. (Grant & Grant, 2010) c. Define Competencies: Clearly define each competency, specifying the expected level of performance and the conditions under which it should be demonstrated. (Marzano, 2006) d. Align with Instruction: Ensure that instructional activities, resources, and assessments are aligned with the identified competencies. (Tomlinson, 2000) Example Performance Standard: Students will be able to solve algebraic equations. Competencies: Identify the variables and constants in an equation. Apply appropriate algebraic operations to isolate the variable. Check the solution by substituting it back into the original equation. Solve equations with different levels of complexity, including linear, quadratic, and rational equations. TOPIC 3: Articulation of Performance Competencies into Learning Targets Learning competencies are the specific skills and abilities that students need to demonstrate in order to meet the performance standards. Competencies may be broad or specific, and may include both content knowledge and skills such as problem-solving, critical thinking, and communication (Romero & Ungria, 2022). The Importance of Articulation Clarity and Focus – Articulating performance competencies into learning targets helps clarify educational goals for both teachers and students. This clarity ensures that all stakeholders understand what is expected, which enhances focus during instruction. When learning targets are well-defined, students can better grasp the purpose of their activities and assessments. Alignment with Standards – This articulation process ensures that learning targets align with broader performance standards set by educational authorities. By connecting specific competencies to overarching standards, educators can ensure that their teaching practices contribute meaningfully to students’ overall educational development. Enhanced Assessment – Clearly articulated learning targets facilitate more effective assessment strategies. When educators know exactly what competencies they are assessing, they can design evaluations that accurately measure student understanding and skills. This alignment also allows for formative assessments that guide instructional adjustments throughout the learning process. Steps in Articulating Performance Competencies into Learning Targets 1. Identify Performance Standards. Begin by reviewing the relevant performance standards that outline the expected skills and knowledge for the subject area. This provides a foundation for determining what competencies need to be developed. 2. Define Competencies Break down the performance standards into specific competencies. These should encompass not only the knowledge required but also the skills needed to apply that knowledge effectively. 3. Develop Learning Targets Translate these competencies into clear, measurable learning targets. Use action verbs from Bloom’s taxonomy to ensure that targets reflect observable behaviors (e.g., "solve," "analyze," "create"). 4. Align Instructional Strategies Design instructional activities that directly support the achievement of these learning targets. Ensure that teaching methods are varied and engaging to meet diverse student needs. 5. Create Assessment Tools Develop assessments that align with both the performance competencies and the learning targets. This could include quizzes, projects, or practical applications of mathematical concepts. 6. Review and Revise Continuously evaluate the effectiveness of both instruction and assessment in achieving the articulated learning targets. Use feedback from assessments to refine teaching strategies and learning objectives. Conclusion The discussion on performance standards, competencies, and learning targets in mathematics provides a comprehensive framework essential for effective teaching and assessment. By clearly defining performance standards, competencies, and objectives, educators can establish a structured approach to student learning. Performance standards set the benchmarks for achievement, while competencies translate these standards into actionable skills and knowledge that students must develop. The ABCD method of writing objectives enhances clarity and specificity, ensuring that educational goals are measurable and aligned with desired outcomes. This method not only helps in formulating clear objectives but also ties into Bloom's Taxonomy, enabling educators to address different levels of cognitive complexity in their teaching. Articulating performance standards into competencies and subsequently into learning targets allows for a more focused instructional approach. This breakdown clarifies educational expectations for both teachers and students, facilitating a better understanding of what needs to be achieved. Moreover, the alignment of competencies with instructional activities ensures that teaching is directed towards meeting the standards. Well-defined learning targets enhance assessment strategies, making it easier to measure student understanding and adapt teaching methods accordingly. The process of reviewing and revising instructional strategies based on assessment outcomes ensures that teaching practices remain effective and responsive to student needs. This ongoing evaluation fosters a culture of continuous improvement in mathematics education. In summary, the effective articulation of performance standards into competencies and learning targets is crucial for fostering an environment where students can successfully acquire and apply mathematical knowledge and skills. This structured approach not only enhances educational clarity but also contributes significantly to student achievement and engagement in mathematics. UNIT 4 Title: Authentic Assessment Methods in Mathematics Education (by Saba and Canson) Topic 1: Project-based Assessment The use of project-based assessment techniques has continued to grow within education curriculums as resources and concepts beyond traditional testing applications have evolved. There can be extensive value to the student's overall learning process with the addition of project- based learning to supplement standard curriculum material. Often the project-based component of a lesson plans can help to make the concepts relatable for students (“How to Use Project- Based Assessments (PBAs) in Education,” 2023). Effectively Utilizing Project-Based Assessments Project-based assessments are an opportunity to utilize and measure the higher order thinking skills of students. A project-based assessment will apply multi-faceted skills to be encompassed into a cumulative project. This can be a singular project at the end of a grading period or it can be done at designated intervals throughout the marking period. The intent is to design the project- based assessment to encompass the lesson plans, teacher worksheets and any additional teacher resources which will ultimately provide a physical example of what was has been learned and what can be applied by the student. Advantages of Project-Based Assessments Some benefits of project-based assessments include the overall vantage point of subject correlation with industry applications. For example, students learning traditional uses of mathematic formulas or physics theories may benefit from studying the use of these topics in everyday life. The idea behind a value-added project-based assessment is to strengthen the understanding of the lesson plans through experiencing the subject matter in a relevant way. Expressive educational areas such as the arts, are especially an area where the creativity of a project can be largely left up to the endeavors of a student. However, overall, the teacher has the responsibility to develop adequate worksheets and lesson plans to support the central ideas or techniques surrounding the projects. Examples of PBA (Project-based Assessment) According to “How to Use Project-Based Assessments (PBAs) in Education” (2023), in classrooms that use PBL, students often work together to answer curriculum-relevant questions and solve challenges, preparing them to become adept communicators and collaborators in their future lives and careers. Instead of end-of-unit tests, they are assessed through group or independent projects. Presentations Labs and experiments Physical crafts and creations Written reports Classroom debates or mock trials  Plays and performances Journals, blogs, or photo logs Videos or podcasts Plans, strategies, or campaigns Sample Scenario 1. In a geometry project, students will create a blueprint for their dream bedroom. They will start by measuring the dimensions of their actual bedroom or a designated space in the classroom. Using graph paper, they will draw a scaled layout of the room, including furniture like beds, desks, and shelves. Students will calculate the area of the room and the area of each piece of furniture to ensure everything fits nicely. They will also determine the perimeter of the room to understand how much wall space is available for decorations. Finally, students will present their blueprints to the class, explaining their design choices and calculations. 2. For a statistics project, students will analyze their classmates' lunch preferences. They will start by creating a simple survey with questions about favorite foods and dietary restrictions. After collecting responses from their peers, they will calculate the mean, median, and mode of the data to find out which foods are most popular. To make their findings clear, students will create bar graphs or pie charts to visualize the results. They will then present their analysis to the class, sharing insights from the data they collected. PBAs differ from tests and quizzes, which can fall short in deciphering between actual knowledge and rote memorization. Instead, they (PBAs) help students build knowledge and challenge them to apply their new knowledge in meaningful ways. Topic 2: GRASP Framework GRASPS is a model advocated for by Grant Wiggins and Jay McTighe to guide teachers in designing authentic performance-based assessment. It’s a form of assessment that engages learners to employ their thinking skills and demonstrate application of essential knowledge, conceptual understanding, and skills acquired throughout a unit of learning (Alison, 2021). To help educators construct authentic assessment, Wiggins and McTighe’s came up with GRASPS model. GRASPS is an acronym for teachers to: COMPONENT DESCRIPTION Goal Defines the problem or challenge that students are expected to resolve. It provides clarity on the learning outcomes. Role Specifies the persona or position the student will assume to accomplish the task, often reflecting real-world applications. Audience Identifies who will receive or evaluate the student’s work, adding significance to the task. Situation Provides context for the task, helping students understand its relevance and real-world application. Product/Performance Outlines what students will create or perform to demonstrate their understanding and skills. Standards Establishes the criteria for success, including rubrics that will be used to assess student performance. Example: GRASPS Model for Statistics: Grade 7 Task Title: Analyzing School Lunch Preferences  COMPONENT DESCRIPTION Goal Students will analyze data collected from a survey about their classmates' lunch preferences to determine the most popular lunch items and identify trends. Role Students will act as data analysts working for the school cafeteria to improve lunch offerings based on student preferences. Audience The audience will be the school administration and cafeteria staff, who will use the findings to make informed decisions about menu changes. Situation The school cafeteria has received feedback that some lunch items are not popular among students, and they want to ensure that meals meet student preferences. Product/Performance Students will create a report summarizing their findings, including graphs (bar charts or pie charts) to visually represent the data, and present their recommendations for new lunch items. Standards Assessments will be based on a rubric evaluating the accuracy of data analysis, clarity of graphs, quality of recommendations, and effectiveness of the presentation. Task Steps 1. Survey Design - Create a simple survey asking classmates about their favorite lunch items, dietary restrictions, and any suggestions for new options. 2. Data Collection - Distribute the survey to classmates and collect responses. 3. Data Analysis - Organize the collected data using tally charts or frequency tables. - Calculate percentages for each lunch item preference. 4. Graph Creation - Use graphing software or hand-draw bar charts and pie charts to visually represent the data. 5. Report Writing - Write a report that includes: - An introduction explaining the purpose of the survey. - A summary of findings with graphs. - Recommendations for new lunch items based on student preferences. 6. Presentation Phase - Prepare a presentation to share findings with classmates or simulate presenting to the school administration. - Use visual aids like posters or digital slides to enhance communication. 7. Reflection - After presentations, discuss what was learned about data analysis and how it can influence real-life decisions in a school setting. Assessment Criteria Data Accuracy (30%) – Correctness in data collection and analysis. Graphical Representation (30%) – Clarity and appropriateness of graphs used. Quality of Recommendations (20%) – Relevance and feasibility of suggested lunch items. Presentation Skills (20%) – Effectiveness in communicating findings to the audience. This task engages students in practical applications of statistics while developing their analytical skills and understanding of data representation. Topic 3: Three Modes of Authentic Assessment: Observation, Performance Tasks, and Actual Performance Authentic assessment is a crucial aspect of modern education, focusing on evaluating students' abilities in real-world contexts. The three primary modes of authentic assessment—Observation, Performance Tasks, and Actual Performance—each serve unique purposes and provide valuable insights into student learning. This discussion explores these modes in detail. A. Observation Definition Observation involves systematically watching and recording students' behaviors, interactions, and performance over time. It allows educators to gather qualitative data about student engagement, skills, and attitudes in a natural setting. Purpose The primary goal of observation is to assess students' ongoing learning processes rather than just their final products. This mode helps teachers identify strengths and weaknesses in students' understanding and skills. Implementation Regularity – Observations should be frequent and consistent to track progress effectively. Documentation – Teachers should maintain detailed records of their observations to inform instruction and provide feedback. Tools – Various tools can be used for observation, such as developmental checklists or interview sheets that guide the assessment process. Benefits - Provides immediate feedback to students. - Allows for the identification of learning styles and needs. - Facilitates a deeper understanding of student behavior in different contexts. B. Performance Tasks Definition Performance tasks require students to demonstrate their knowledge and skills through tangible products or performances. These tasks are designed to mimic real-world challenges that students may face outside the classroom. Purpose The aim is to assess not only what students know but also how they apply their knowledge in practical situations. This mode emphasizes critical thinking, creativity, and problem- solving skills. Implementation Design – Tasks should be open-ended, allowing for multiple approaches and solutions. Assessment Criteria – Clear rubrics should be established to evaluate the quality of the work produced. Examples – Common performance tasks include projects, presentations, or portfolios that showcase a student's learning journey. Benefits  - Encourages active engagement and ownership of learning. - Provides a comprehensive view of student capabilities beyond traditional testing methods. - Fosters collaboration and communication skills through group projects. C. Actual Performance Definition Actual performance assessments involve measuring students' abilities during specific tasks or events at designated times. This mode often includes demonstrations of skills in real-time scenarios. Purpose The focus is on assessing how well students can perform specific tasks under observation, such as singing, acting, or conducting experiments. This mode captures the dynamic nature of student learning. Implementation Setting – Assessments can take place in various environments, such as classrooms, labs, or performance venues. Assessment Methods – Tools like performance checklists or oral questioning can be employed to gauge student understanding during the task. Examples – Actual performance assessments can include science experiments, art performances, or physical education activities. Benefits - Provides immediate insight into student capabilities under pressure. - Allows teachers to assess not only knowledge but also application in real-time scenarios. - Encourages self-reflection as students evaluate their own performances. Conclusion The GRASP framework, developed by Wiggins and McTighe, further guides educators in creating authentic performance-based assessments. This model emphasizes defining clear goals, roles, audiences, and situations while outlining expected products and success criteria. For instance, in a statistics project, students might act as data analysts creating reports on lunch preferences based on surveys. Lastly, the discussion explores three modes of authentic assessment: Observation, Performance Tasks, and Actual Performance. Observation involves systematically recording student behavior to assess ongoing learning, while Performance Tasks require students to demonstrate knowledge through tangible outputs, fostering engagement and collaboration. Actual Performance assessments measure student abilities in real-time, offering immediate insights and encouraging self-reflection. Overall, these methods aim to provide meaningful learning experiences that reflect real-world applications in mathematics education.  REFERENCES Anderson, L. W., Krathwohl, D. R., & Bloom, B. S. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives. New York, NY: Longman. Grant, C. A., & Grant, M. G. (2010). Differentiated instruction: A practical guide for teachers. Corwin Press. https://us.corwin.com/books/diff-instruct- strategies-pro-3e- 241133 Gosselin, D. (2017). Competencies and learning outcomes. InTeGrate: SERC. https://serc.carleton.edu/integrate/programs/workforceprep John Hopkins University. (2024). Writing effective learning objectives/ educational objectives. Office of the Provost. https://provost.jhu.edu/ education/institutional- assessment/assessment-at-jhu/assessment-measures/writing-effective-and- measurable-learning-objectives. Marzano, R. J. (2006). Classroom management that works: Techniques for creating a positive and productive learning environment. ASCD. https://perino.pbworks.com/f/4%20CLM-Basic-Text(M).pdf ProctorEdu (2020). Definition of Performance Standards. https://proctoredu.com/glossary/performance-standards Romero, A. J.,& Ungria, C. A. (2022) Articulation of performance standards into competencies. CourseHero https://www.coursehero.com/file/150820930/ Articulation-of- Performance-Standards-into-Competencies Tomlinson, C. M. (2000). Differentiation in action: Case studies of inclusive classrooms. Allyn & Bacon. https://www.tandfonline.com/doi/full/ 10.1080/13603116.2020.1813450 Wiggins, G. P., & McTighe, J. B. (2005). Understanding by design. Association for Supervision and Curriculum Development. https://ascd.org/books/ understanding-by- design-expanded-2nd-edition?variant=103055 Ago, H. #steemiteducation 5 Y. (2018, January 29). Education: Three Modes Of Authentic Assessment. Steemit. https://steemit.com/steemiteducation/@heartmich/education- three- modes-of-authentic-assessment-a0314f51f7143 Alison. (2021, December 27). GRASPS Assessment design and student Metacognition - alisonyang.com. alisonyang.com. https://alisonyang.com/grasps-assessment-design- and- student-metacognition/ How to Use Project-Based Assessments (PBAs) in Education. (2023). How to Use Project- Based Assessments (PBAs) in Education. https://propello.com/blog/how-to-use- project-based- assessments-pbas-in-education Karnasih, I. (2014). AUTHENTIC ASSESSMENT OF STUDENT LEARNING MATHEMATICS WITH TECHNOLOGY. https://eprints.uny.ac.id/24918/1/2.pdf Project Based Assessment. (n.d.). Www.teach-Nology.com. https://www.teach- nology.com/currenttrends/alternative_assessment/projectbased.html Articulating Learning Goals. (2014, July 8). Www.swarthmore.edu. https://www.swarthmore.edu/assessment/articulating-learning-goals Burgos, H. (2024, January 31). Statistics Project Topics: From Data to Discovery. Papersowl. https://papersowl.com/blog/statistics-project-ideas Choudhary, R. (2022, October 8). 75+ Realistic Statistics Project Ideas To Score A+. https://statanalytica.com/blog/statistics-project-ideas/ Doc Mart. (2021, September 23). Performance Standards, Competencies, and Learning Targets in Mathematics. YouTube. https://www.youtube.com/watch?v=9Ml5oRV_Ywc GRASP Framework Overview – GRASP Open. (2014). Grasp-Open.com. https://www.grasp- open.com/doc/ch04.php/ Kurt, S. (2019, April 24). Using Bloom’s Taxonomy to Write Effective Learning Objectives: The ABCD Approach. Educational Technology. https://educationaltechnology.net/using- blooms-taxonomy-to-write-effective-learning-objectives-the-abcd-approach/ MindTools | Home. (n.d.). Www.mindtools.com. https://www.mindtools.com/acqerdm/abcd- learning-objectives-model Revisiting GRASPS: a model for project based learning. (n.d.). Aidan Hammond. http://www.aidan-hammond.net/new-blog/2021/9/24/revisiting-grasps-a-model-for-project- based-learning Statistics Project Ideas for Students - AssignmentBro. (2022, September 19). Assignmentbro.com; Scotch Scotch scotch. https://assignmentbro.com/blog/statistics- project-ideas Using GRASPS tasks to create authentic assessment. (n.d.). https://www.canberra.edu.au/research/faculty-research-centres/csc/archive/family-farm- teams-program/teachers-resources/teaching-strategies-information-sheets/Creating- authentic-assessment-taks-using-GRASPS.pdf Vector Solutions. (2020, May 6). ABCD: The Four Parts of a Learning Objective. Vector Solutions. https://www.vectorsolutions.com/resources/blogs/abcd-the-four-parts-of-a- learning-objective/ Yang, A. (2019, December 7). GRASPS Assessment Design and Student Metacognition - alisonyang.com. Building Learning Agility. https://alisonyang.com/grasps-assessment- design-and-student-metacognition/ Yoder, N., & Dusenbury, L. (2017). A Process for Developing and Articulating Learning Goals or Competencies for Social and Emotional Learning. https://casel.s3.us-east- 2.amazonaws.com/CASEL-Resources-Developing-Articulating-Goals.pdf (2024). Hawaii.edu. https://www2.hawaii.edu/~jconey/proj2/ABCDmodel.doc