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right000KY Skills U Classroom Observation ToolInstructional Indicators and Their Respective Mathematics Sample IllustrationsInstructional IndicatorsMathematics Sample IllustrationsA. Lesson content is based on standards and learner goals.1. Teaching and learning are focused on a targeted set of standards that builds on their natural connections.In an Adult Basic Education (ABE) lesson on fractions, the instructor introduces the lesson by reviewing what was learned in the previous day’s lesson and stating what students will be able to do by the end of today’s lesson. During lesson activities, learners demonstrate appropriate math practices as they use the number line to compare and explain equivalency between fractions and decimals. At the end of the lesson, learners assess the standards and "I can" statement to determine the learning for that lesson.2. The lesson has an explicit, standards-based objective and purpose, stated in terms of the desired student learning outcomes.During the introduction of a geometry lesson, the class reads the "I can" statement aloud in unison. Example: “I can find the distance between two points in a coordinate grid by using the Pythagorean Theorem.” After working together to solve a small set of problems, learners are given a set of problems to work on individually in a specified time followed with a discussion of how this skill could be used on the job.3. Students use level-appropriate resources and materials directly related to the targeted standards.During a training in screen film image processing, rather than moving through the textbook page by page, the students focus on those pages in the textbook that address the learning standards. The majority of the learning time is dedicated to understanding the concept of ratios, proportions, and functions, which takes substantial explicit instruction, problem-solving, and exercise. In comparison, less learning time is allotted to the less demanding standards.4. Lesson content connects to learners’ goals, interests, or needs, and is applicable to their lives. Given a set budget, learners are asked to use a calculator to determine how they might best utilize their budget to purchase new school clothes and supplies for their children. They use ads from stores to calculate discounts for best buys. Learners then compute applicable taxes to determine the money owed to see which items they can afford. Learners share their strategies and results with other class members.5. Students are made aware of the connections among the content and objectives of current, previous, and subsequent lessons throughout and at the close of the lesson.In an Adult Basic Education (ABE) math class, the instructor starts each daily session with a sample problem from the previous day's material, then uses each student's response to gauge the individual's grasp of the concept. If students are unclear about any of the material, this provides the instructor an opportunity to reteach the lesson material or provide individual assistance. At the end of a lesson, the students review the purpose of the lesson, summarize their own learning, and are introduced to what they will be working on next. B. Lesson delivery engages students.1. Lesson is communicated clearly with regard to directions, content, questions, and evaluations of student work and ideas.Learners in an Adult Secondary Education (ASE) algebra class learn about the day’s lesson as the instructor reads the student target statement from the PowerPoint displayed on the class SMART board and makes a connection to the previous lesson’s student target. During the lesson, directions for the activities appear in the PowerPoint as the instructor explains them and entertains questions. As learners work to complete the activities, the instructor circulates among the learners, asking probing questions and prompting them to explain their thinking. Before leaving the lesson, learners reflect on their learning by writing in their journal what they understood about the lesson content and what needs clarification.2. Lesson delivery is varied in presentation, instructional activities, and examples to improve classroom interaction, student engagement, conceptual understanding, and skill development.Students build on prior knowledge to increase their understanding of ratios and proportional reasoning in a lesson that centers on a cooking scenario. The lesson begins with a brief introduction, in which the instructor proposes a basic sugar cookie recipe containing flour and sugar. As a large group, students work with the teacher to discuss the different ways we mathematically express a “ratio” of the flour and sugar in the recipe. Emphasizing that the recipe should still taste the same, the group discusses how the ingredient amounts change if the recipe needs to be doubled or halved. The instructor explicitly explains that these different ratios are “proportional”, and students discuss this new idea of equality. In smaller groups, students then rotate among several activity stations. These stations include problems where students must adjust recipes with different ingredient amounts and record the values in a table; determine scale (how much larger or smaller) among different recipe ratios; work with a recipe with a different flour-to-sugar ratio; record both recipes on a graph; determining which recipe is “more sugary;” explore “challenge” questions like what the steepness of the graph has to do with taste.3. Students have various opportunities (beyond worksheets) to apply new learning in authentic or practical adult-oriented contexts.Learners work on a design problem during a lesson on measurement. They are given a certain number of wall sections of a certain height and width so that they can create a variety of rectangular, prism-shaped toolshed designs. Learners sketch the possibilities and determine the measurements that will maximize the floor area and capacity of the shed.4. Students have appropriate hands-on opportunities to interact with computers, the Internet, and other digital media.In an Adult Basic Education (ABE) class, the bell-ringer activity has learners logging in to EdReady on computers or iPads to preview the day’s topic. When time is called, their attention is turned to the instructor’s power point. During the lesson, individual learners have opportunities to use the SMART board tools to answer assigned problems while the rest of the class uses calculators to check their work. Student access their follow up assignment using their Edmodo account. 5. Students are consistently or often given appropriate wait time (3 or more seconds) before being prompted for a response to a question. As the instructor leads learners through a series of ratio/proportion problems, he/she poses questions to the entire class. Learners are instructed not to answer immediately, but to wait to be recognized, giving everyone ample time to consider their response. When learners have difficulty responding to a question, rather than supplying the answer and moving on, the instructor asks a related easier question, thereby building reasoning until the answer to the original question becomes apparent. C. Learning is monitored and instruction adapted.1. Student understanding is consistently checked throughout the lesson through informal yet deliberate methods used by the instructor (e.g., walks around the room to check on students’ work, monitors verbal responses, etc.).During an algebra lesson, learners create models using algebra tiles or other manipulatives to demonstrate understanding. The instructor circulates among the learners, interacting with them through questioning. Learners are asked to explain their models to their table partners and encouraged to ask questions about the other’s model. At the end of the lesson, learners display their red, yellow, or green cards to indicate their level of understanding.2. Instruction is adjusted according to students’ demonstration of understanding (e.g. re-presenting, re-teaching, modeling, etc.).As the instructor delivers new information in an Adult Basic Education (ABE) class, he/she monitors for understanding by watching learners’ facial reactions and by assessing the level of questions asked, the degree to which procedures are followed, and learners’ willingness to do the work assigned. When the instructor sees that a learner is struggling to complete an activity that uses manipulatives, learners are paired. The struggling learner listens carefully and moves the manipulatives as the second learner only speaks the process. The instructor then asks clarifying questions to be sure solution is clear.3. Students are often given prompt, specific feedback to correct misunderstandings and reinforce learning.As a bell ringer activity in an Adult Secondary Education (ASE) class, the learners are asked to agree or disagree with the shown problem and solution and to explain their reasoning. As multiple explanations are given, learners whose reasoning was faulty are given opportunities to change their original decision. During class, learners solve problems and show their work. The most difficult problems that instructor has observed are re-created on board and students with solid understanding are encouraged to explain their solutions.4. Struggling learners, as well as learners who would benefit from extra challenges, have opportunities for supplemental activities and materials that meet their needs.After a brief introduction to a topic and a standardized pre-assessment, the class is divided into at least four activity centers. Two tables offer activities pertaining to the newly-presented material, providing guided and independent practice, respectively. Another station provides review material and support for prerequisite skills. The last station provides hands-on application of the newly practiced skill. Students are free to choose their own station, where they will spend one ten-minute session. After two rotations, students will be randomly assigned into four groups where they will collaborate to complete a quiz.5. Students evaluate and reflect on what they learned and how they learned it.At the end of a lesson about measurement, learners record the vocabulary words in their journals, defining the terms in their own words. Before leaving class, they fill out a lesson evaluation form, using ratings to respond to questions about the lesson. At the bottom of the form, they indicate what help they would like to have. D. Learning engages students in higher-order thinking.1. Relevant, thought-provoking questions are posed to stimulate student thinking beyond recall in order to engage learners in inquiry, challenging their own assumptions and encouraging problem-solving.In an Adult Basic Education (ABE) mathematics lesson, learners use tracing paper to compare the angles formed when a transversal crosses a pair of parallel angles. After making comparisons, the learners share their observations and develop a general rule that will be true for all angles formed in these instances.2. Students are consistently expected to elaborate on and justify their responses.An Adult Basic Education (ABE) math instructor facilitates an activity where students take turns placing small placards with decimal, fraction, or percent amounts on an open-ended number line. Students answer questions like, "Can you tell us why you placed 1/2 to the right of 3/7?," "Why isn't 1/2 to the left of 3/7-- 1 is less than 3 and 2 is less than 7, right?," or "What other quantities could go in the same spot as 1/2? Why?"The instructor makes use of these types of questions so that students give responses that are elaborative and clarifying.?Students are able to practice articulating their thoughts with evidence and reasoning, and their verbalizations will help the other students improve their conceptual understanding. The lesson's focus is on the reasoning and validations used in arriving at solutions, not on the solutions alone.3. Students participate in activities that require suspending judgment, coming to consensus, discussing alternatives, prioritizing, negotiating, problem-solving, evaluating, and other skills.Working together to plan a GED? graduation ceremony, table partners must divide up the work, negotiate budget needs, come to consensus about the theme, place, invitees, displays etc. When consensus is reached, one partner does the actual writing without talking while the other partner instructs the partner what to write. Next the partners evaluate their plan together and make adjustments as needed.4. Students are encouraged to voice ideas and opinions without fear of negative consequences.Students of an Adult Secondary Education (ASE) class learn through daily interactions with their teacher that trying out ideas, being uncertain, and struggling are a normal part of the learning process. Learners are praised for effort and resilience rather than for providing “correct” answers. When they make mistakes, learners are reminded of how much can be learned both from errors and correct responses rather than facing embarrassment or disappointment.5. All or most students display persistence with challenging tasks.Learners in an Adult Secondary Education (ASE) math classroom use the seven pieces (five triangles, one square, and one rhomboid) of a tangram to make a picture of a cat. Learners are advised that all pieces must be used, must not overlap, and must be laid flat. Learners are only given the silhouette of the cat as a reference. Students complete the task individually, but are arranged in tables so that those who struggle may seek support from others in order to complete the task.E. Lesson is contextualized to equip students with the skills and dispositions needed for workforce success.1. Classroom activities include opportunities to learn and practice the E Standards listed in the lesson plan.The list of E Standards is displayed prominently in the classroom and (periodically throughout the lesson) the instructor leads a discussion about which of the E Standards have been applied in the activities. Using a Venn diagram with 3 sections, the class lists which of the E Standards were demonstrated by the instructor, the students, or both.?2. Students work in pairs or small groups on assignments, projects, or presentations to model professionalism in workplace communication.A class has partnered with a local youth shelter to identify a need (purchasing a van, or building a storage structure for outdoor equipment). During a math lesson, Adult Basic Education (ABE) students brainstorm and establish ground rules for working together effectively and efficiently to develop realistic and mathematically sound solutions for this need. The ground rules are then measured using a rubric or scoring matrix developed by the class with criteria (e.g., everyone should assume a fair share of the work, or members should not be passive or act indifferent to the task at hand).The instructor explicitly models and explains how the selected E Standards relate to the academic content and prepares students for job opportunities in their local communities.During an Adult Secondary Education (ASE) class, either by self-selection or random assignment, students research and choose one current job posting and description (posted on employers’ websites, Kentucky Career Centers, Focus Career, or the local want ads) in the local community. Next, using a list of NCRC Level 3 skills, students check which math skills are needed to be successful in the job. ?Finally, they list the E Standards that would be most applicable to the chosen job. NCRC MathE StandardsSolve problems that require a single type of mathematics operation (addition, subtraction, multiplication, and division) using whole numbersAdd or subtract negative numbersChange numbers from one from to another using whole numbers, fractions, decimals, or percentagesConvert simple money and time units ( e.g. hours to minutes)4. Instruction includes examples of how one or more of the E Standards apply to jobs in the local community.For a lesson on interpreting graphic data representations, students in an Adult Secondary Education (ASE) class research local job opportunities to determine which jobs are most in demand. Based on the number of ads for each job, they select the top three jobs and assign a different color post-it pad for each. Next, each student is assigned a color and quickly brainstorms 10 soft skills needed for success in that job, writing one per sheet. Post the 10 E Standards around the room and have students place each post-it beneath the E Standard with which it most closely aligns. Using three different colors provides a visual representation of the distribution of the most highly sought skills, which the students then represent by creating bar graphs and pie charts.5. The lesson culminates with an opportunity for student reflection of how they will apply employability skills outside of the classroom.At the conclusion of a lesson on fractions, students are asked to work in pairs to research and list five ways in which fractions are used in one of Kentucky’s top employment sectors (Healthcare; Manufacturing; Transportation; Distribution and Logistics; Construction and Trades). Each pair shares their list of tasks to determine where commonalities exist to illustrate that fractions are integral to every workplace. Mathematics Lesson Indicators (CCR SIA Math)1. Students engage in Standards for MP that are central to the goals of the lesson and connected with the targeted content.An Adult Basic Education (ABE) math instructor begins a new managed class cycle with the goal of helping students build confidence in their ability to contribute. He wants to instill MP #1 (make sense of problems and persevere in solving them) in his first lesson. He begins the class with a series of three diagrams of sports balls. Each of the three diagrams shows a variety of sports balls with varying weights. Students collaborate to discuss and answer the questions, “What do you notice about the three diagrams? What do you wonder about the three diagrams?” Student comments show they are trying to make sense of the problem before they rush to solve it. Students then pursue further exploration of the problem by reasoning their way through the calculation of the ball weights, utilizing the “ask a friend” strategy when they get stuck.2. The lesson targets one or more aspects of rigor (conceptual understanding, procedural skill and fluency, or application), as appropriate for the addressed standard(s).Mark the aspect(s) of rigor the lesson addresses:?Conceptual Understanding ?Procedural Skill and Fluency?ApplicationStudents develop conceptual understanding by watching an Adult Secondary Education (ASE) math instructor demonstrate that a fraction a/b as a quantity is formed by a parts of a fraction with the size 1/b. the instructor can write 3/5 as three sets of 1/5. The instructor draws tic marks on a cup, dividing it into five equal portions and shading in three of the portions. The instructor then shows three more of the same cups with only one portion shaded in. Finally, the instructor will mark on a number line (adequately sized to show fractions of 1) where three-fifth (and each fifth) occurs. Students then generate other real-life examples of situations where unit fractions combine to create larger fractions, as well as when larger fractions should divide into unit fractions. Students then place their illustrations on a number line, showing the unit fractions combining to create the larger fraction 3. Students are presented with high-quality, challenging questions and problems that prompt them to discuss their developing thoughts about the lesson content.An Adult Secondary Education (ASE) math instructor builds numeracy by posing a series of questions about the relationship between the numbers 2 and 6. The series creates an intentional learning progression because the instructor first asks, “How would an additive thinker describe the relationship between 2 and 6?” (Answer: The relationship demonstrates an increase of 4.) Then the instructor asks, “How would a multiplicative thinker see the relationship between 2 and 6?” (Answer: The relationship demonstrates 2 being multiplied by 3 to get 6.) “How would a proportional thinker see the relationship between 2 and 6?” (Answer: students who think proportionally know that a group of 2 children growing to 6 children would be equivalent to a group of 100 children growing to 300 because they see numbers in relative terms, rather than absolute terms.)4. Mathematical concepts are made explicit through explanation, modeling and/or examples.An Adult Secondary Education (ASE) Math Instructor wants her students to develop geometric reasoning skills. Prior to covering formulas for calculating surface area, she explains and demonstrates the use of electronic nets (shapes that form by unfolding three-dimensional figures) to virtually “unfold” geometric figures. Students work individually to fold and unfold paper nets of 3-dimensional shapes. They then assign dimensions to the shapes and calculate surface area. 5. Precision is demonstrated and expected regarding mathematical calculations, terminology, symbols, graphs, etc.Students play a matching game to demonstrate mastery of precise geometry terminology. Students compete in small groups to match cards showing a particular shape with the appropriate definition card and label card, in a timed environment. Source: Adapted from Office of Career, Technical, and Adult Education’s Adult Teacher Competencies. ................
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