•PICTURES: Pictures are mathematical representations. Pictures provide a useful strategy that will help with your explanation (this may include but is not limited to: pictures, charts, graphs, t-tables, and the use of manipulatives). Encourage students to think about different materials/manipulatives that would be useful to help solve the problem. • VERBAL OR WRITTEN EXPLANATIONS: Once the child has worked through the task encourage her/him to include a detailed verbal or written explanation. At least one sentence or phrase for K–2, t wo to four sentences for 3–5, summarizing what they have done. ‘Words’ also includes labeling the work and using appropriate mathematical vocabulary and symbols, allowing the teacher to follow the child’s thinking. At the K–2 level student explanations will be more verbal. Teachers should encourage students to ‘talk through’ the mathematics using manipulatives or describing pictures they have drawn. As students gain experience solving performance tasks their communications skills will improve. Teachers should allow students additional time to work on the written component of performance tasks, which can easily be integrated, into a daily writing program. • EQUATION/NUMBER SENTENCE: This involves the actual strategy the child has chosen to solve the problem. It is the equation or mathematical sentences. There are a number of different ways to solve each of the tasks, so the child is encouraged to include all of the steps s/he used to solve the problem. Students should consider if their answer is reasonable and consider why or why not. If the student wants to become an expert on the problem, s/he must present their solution in more than one way, relate it to other situations, and/or generalize the concept (i.e. state a rule or create an equation).

NAPE Understanding

Reasoning, Strategies and Mathematical Procedures

Communication

Novice Apprentice Practitioner Expert Holistic Score? The holistic score is a single score used to rate a complete task as a whole. One rating on the NAPE (Novice, Apprentice, Practitioner or Expert) scale summarizes the student’s full performance. The teacher must consider all of the aspects of the student work for the task when assigning a NAPE score. SCORING TIP: It is helpful to assign the analytical score before the holistic score so the teacher can determine the student’s strengths and weaknesses in relation to their knowledge of the problem. What is the Analytical Score? The analytical score breaks down the student’s thinking into three areas: the student’s understanding of the concepts in the problem; the reasoning, strategies, and mathematical procedures they used to solve the task; and the communication of their work. As the teacher analyzes the student work, they must determine the student’s performance level for each component. The teacher needs to look at each of these areas and determine what the child does or does not know, and can or can not do; and then assign a NAPE (Novice, Apprentice, Practitioner or Expert) score based on the child’s performance in that area.

Understanding:

The student understands the question(s) the problem poses. The student chooses information that is relevant to solving the problem. When the student uses graphs or pictorial representations they show an accurate interpretation of the problem. The student can restate the problem in his or her own terms. Reasoning, Strategies, and Mathematical Procedures: The student chooses an appropriate and applicable strategy to solve the problem. The student chooses an appropriate mathematical procedure to solve the problem. The strategy presented communicates a reasoning process that is logical and sequential. The student’s strategy draws from past knowledge and experience. The student uses a system to check accuracy and precision. Communication: The results are presented clearly, coherently and accurately. The student uses tools of mathematical communication. These tools include but are not limited to: words, phrases and sentences; labels; mathematical symbols and notations; equations; graphs; and pictures. The student shows correct use of mathematical terms and uses them whenever appropriate.

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