APPLYING THEORIES Task 2
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183
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Mathematics
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Jan 9, 2024
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APPLYING THEORIES, DESIGN PRINCIPLES, AND EVALUATION MODELS D183- Task 2 Western Governors University Crystal Herring November 2023
A1. Curriculum: Title:
Envision Mathematics Common Core Creator:
Savvas Learning Company Content:
Mathematics Grade:
K Goal/ Objectives:
The goal of the mathematics envisions curriculum is to support students with mathematic skills by providing them with mathematics concepts, vocabulary, and modeling skills. According to the Savvas company, “
Envision Mathematics is designed to achieve a coherent progression of mathematical content within each course and across the program, building lesson to lesson” (2023). A2. Design Principles: Two design principles that Envisions adheres to is Intergration and Sequence. Intergration is demonstrated throughout the curriculum when it comes to having to have prior knowledge skills of the previous lesson in order to move on to the next. “
Building from students’ prior knowledge, connecting topics that used to seem unrelated, and applying these skills to solve new problems (Ferguson, 2017). In the beginning of each lesson of the teacher edition, it would give an option to reteach the previous lessons for students who were struggling with that topic. It also shows a students should know sections of the teacher manual, which helps the teacher to assess her class on what they should know prior to starting the lesson. Intergration of topics is important because students should continue to keep prior knowledge skills of other topics, which can then be
integrated into another topic. For example, if students are learning about composing numbers that make 10. That same concept could be carried over to the topic of addition. Now students would be able to use what they have learned about composing numbers which then turns into now knowing the numbers that add up to 10. The second design principle is sequencing. Sequencing within the curriculum helps to demonstrate how the curriculum is formed. It shows the layout of the envisions math program formed around major topics students should learn based on their grade level. According to Explore Learning, it states, “Th
e sequence
refers to the particular order of teaching. Teachers have the complete pathway for mathematical knowledge and understanding when paired with the standards
” (2023)
. I think it is most important to teach principal topics in the beginning the year because students would need these principal topics to make connections to the sub-topics. The envisions curriculum framework is planned out in this exact way the major topics are taught first because going into sub-topics. For example, for kindergarten, the first lesson would be number sense. Students are taught to build on skills of knowing numbers. The next topic would be composing numbers that make 5. Students would have to have prior knowledge skills of counting numbers and grouping objects that form a number. A3. Design Ideology: When it comes to Envision ideologies, they are known for following the Scholar Academic Ideology. According to Michael Schiro, he states, “
A curriculum ideology is a collection of ideas held by an individual or group of individuals regarding the organization and function of schooling
”
(Schiro, 2012). As a teacher you are expected to know what you want your students to learn, how they are going to learn it and the impact of what is taught to them based on assessments. Scholar Academic ideology is the approach most teachers would be taking within
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the classroom. The enVisions curriculum follows this ideology because the lessons are teacher directed. For example, a lesson on making 5 for kindergarten students is very explicit. It shows students step by step what numbers they can compose to create the number 5. They specifically use yellow and red counters to model their answers. Another example is the procedures that the teacher has to follow throughout the lesson. They teacher models, the students practice along with the teacher, then students work independently on the same assignment that was modeled. Students are expected to grasp the concepts and then move on to the next lesson. The teacher will use the assessment after each lesson to give students who struggled with the previous lesson, a reteach. This learning ideology supports the objectives and goals of the curriculum by new strategies, new ways of thinking and approaching those strategies, and assessing the strategies and approaches taught to students. A4. Learning Theory of Design: I think the learning theory demonstrated within the enVision curriculum is constructivism. Students are able to incorporate new information into what they already know. They are able to build on their prior knowledge skills. In the article titled, “What does it mean to for math to be integrated it states
, “
This process is called assimilation, and is the foundation of Jean Piaget’s adaptation process for cognitive development, which is all a part of the complex task of learning
. It is the idea that we learn by incorporating new knowledge into their our pre-existing understanding of a topic
”
. This is demonstrated in the curriculum when the lesson asks for students to “Solve and Discuss”. Previously learned concepts are used to build on new topics. The new topics are taught to students through the method of problem-based learning. Another example of constructivism shown within the enVisions curriculum is the method of scaffolding. Insttructional and intervention supports are used to help students throughout the lessons.
According to the enVisions program it states, “The program’s balanced instructional model provides appropriate scaffolding, differentiation, intervention, and support for a broad range of learners, and is designed to facilitate conceptual understanding of mathematics for students at a range of learning levels
” (2023). a.
This theory is in support of the goals and objectives of the curriculum because in the lessons students are asked to use prior knowledge information and apply it to new concepts. This method helps students become successful in each topic after the next because they are continuously building on the skills from the previous lesson. B.CIPP Evaluation Model: Context:
A need that I would address within the enVisions curriculum is for the program to provide more theoretical understanding. I feel that fluency is very important and will help students to develop a deeper understanding of the concepts. Input:
The components of the curriculum that can help students with theoretical understanding of the vocabulary and materials. This is demonstrated within the problem-based learning section of the curriculum. Students can find support for this area in the beginning of each lesson with the “Solve and Discuss” section. Students are able to connect prior knowledge skills as well can vocabulary words that have been used in previous lessons. A second component of this curriculum that supports theoretical understanding is the 3-Act Mathematical Modeling. Through this component of the curriculum students are able to model and use situations from things that they have seen in their real everyday lives. Students are able to model real time situations which help them to notice that math is seen and demonstrated everywhere.
3. Resources and data would need to be gathered in order to assess the effectiveness of the program. To know more about the intellectual understanding, we would have to collect data from the Solve and Discuss section as well as the 3 Act Math activities within the curriculum. The end of unit assessments should be collected to determine the effectiveness of the program. 4. Process:
This curriculum is used among a number of grade levels. My experience with this curriculum throughout my years of teaching the enVisions curriculum helps me to determine which area would be able to show the effectiveness of the program. The Solve and Discuss sections as well as the 3 Act Math activities, will be able to demonstrate the effectiveness of the curriculum. The assessment data will be able to support the effectiveness of the curriculum. 5. To observe how effective the curriculum is, I will start by gathering data from the Solve and Data section and the 3 Act Math activities section. I will observe while students work and determine what areas were effective and which areas students struggled in with the data from the assessment. 6. Product:
I will compare my data with enVisions data scores done by my previous students. This will help me to compare and contrast the areas that students show most effectiveness. This is done through teacher observation and end of unit assessments. I will take beginning of the year data, mid-year data, and end of year data. 7. Data will be analyzed during our mid-year data meeting. This meeting will be held in order to see the progress students are making throughout the curriculum. Our math assessment coach will review the data and create an excel spreadsheet which will help us to notice the difference in scores from the beginning and mid-year data. This will help to demonstrate the effectiveness of
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the curriculum based on the two activities stated. It will help to decide if the curriculum meets students' needs. Works Cited: Ferguson, Trey. (2017). What does it mean for math to be integrated? EducationNC. https://www.ednc.org/mean-math-integrated/ Savvas Learning Company (2023). K-12 Education Curriculum. Copyright © 2023 Savvas Learning Company LLC. All Rights Reserved. https://www.savvas.com/ Schiro, M. S. (2012). Curriculum theory: Conflicting visions and enduring concerns
. SAGE Publications.
https://wgu-nx.acrobatiq.com/en-
us/courseware/page/wgu_D183_15Nov20_design_curriculum_instruct_I_1/wbp_curriculum_ideologie
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