Kean University Supplemental Mathematics Assessment

Impact on Student Learning

NCTM/CAEP Standards/Element Alignment

Teacher Candidate ______Date ______

Supervisor ______Date ______

Directions: Please indicate the score (Beginning – 1; Capable – 2: Accomplished – 3) of the teacher candidate regarding their competence in the following NCTM Standards/elements. If the candidate scores a 3 (Accomplished), specific examples supporting that score must be supplied in the “comments” section.

1.  Organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing, to multiple audiences. (NCTM/CAEP Standard 2d)

Beginning / Under the teacher candidate’s instruction, students do not demonstrate the ability to organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing, or demonstrate evidence only one time.
Capable / Under the teacher candidate’s instruction, students demonstrate the ability to organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing on 2 – 3 occasions.
Accomplished / Under the teacher candidate’s instruction, students demonstrate the ability to organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing on 4 or more occasions.

Score: ______

Comments:

2.  Demonstrate the interconnectedness of mathematical ideas and how they build on one another. (NCTM/CAEP Standard 2e.i)

Beginning / Under the teacher candidate’s instruction, students demonstrate little or no understanding of the interconnectedness of mathematical ideas and how they build on one another and recognize, or demonstrate that understanding only once.
Capable / Under the teacher candidate’s instruction, students demonstrate the interconnectedness of mathematical ideas and how they build on one another, demonstrating such understanding on 2 – 3 occasions.
Accomplished / Under the teacher candidate’s instruction, students demonstrate the interconnectedness of mathematical ideas and how they build on one another, demonstrating such understanding on 4 or more occasions.

Score: ______

Comments:

3.  Apply mathematical connections among mathematical ideas and across various content areas and real-world contexts. (NCTM/CAEP Standard 2e.ii)

Beginning / Under the teacher candidate’s instruction, students show little ability to apply mathematical connections among mathematical ideas, or across various content areas and real-world contexts, or demonstrate such ability only once.
Capable / Under the teacher candidate’s instruction, students demonstrate the ability to apply mathematical connections among mathematical ideas and across various content areas and real-world contexts on 2 – 3 occasions.
Accomplished / Under the teacher candidate’s instruction, students demonstrate the ability to apply mathematical connections among mathematical ideas and across various content areas and real-world contexts on 4 or more occasions.

Score: ______

Comments:

4. Provide students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace. (NCTM/CAEP Standard 3d)

Beginning / Teacher candidate provides students with no opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace, or provides only one instance of such opportunities.
Capable / Teacher candidate provides students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace in observation on 2 – 3 occasions.
Accomplished / Teacher candidate provides students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace in observation on more than 4 occasions.

Score: ______

Comments:

5. Verify that secondary students demonstrate conceptual understanding; procedural fluency; the ability to formulate, represent, and solve problems; logical reasoning and continuous reflection on that reasoning, productive disposition toward mathematics; and the application of mathematics in a variety of contexts within major mathematical domains. (NCTM/CAEP Standard 5a.i)

Beginning / Under the instruction of the teacher candidate, students demonstrate little or no conceptual understanding; procedural fluency, or show such evidence only once.
Capable / Under the instruction of the teacher candidate, students demonstrate a solid understanding of mathematical concepts; and accurate procedural fluency, demonstrating such evidence on 3 – 5 occasions.
Accomplished / Under the instruction of the teacher candidate, students demonstrate a deep understanding of mathematical concepts and accurate procedural fluency; on more than 5 occasions.

Score: ______

Comments:

6. Verify that secondary students demonstrate the ability to formulate, represent, and solve problems; logical reasoning and continuous reflection on that reasoning, and a productive disposition toward mathematics. (NCTM/CAEP Standard 5a.ii)

Beginning / Under the instruction of the teacher candidate, students demonstrate little or no ability to formulate, represent, or to solve problems; display little logical reasoning, engage in little continuous reflection on that reasoning, or have a productive disposition toward mathematics; or show such evidence only once.
Capable / Under the instruction of the teacher candidate, students demonstrate ability to formulate, represent, and to solve problems; they display logical reasoning, they engage in continuous reflection on that reasoning, and they have a productive disposition toward mathematics, showing such evidence on 3 – 5 occasions.
Accomplished / Under the instruction of the teacher candidate, students demonstrate a superior ability to formulate, represent, and to solve problems; they display accurate logical reasoning, they engage in continuous reflection on that reasoning, and they have a productive disposition toward mathematics, showing such evidence on more than 5 occasions.

Score: ______

Comments:

7. Verify that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains. (NCTM/CAEP Standard 5a.iii)

Beginning / Under the instruction of the teacher candidate, students show little ability to apply mathematics in a variety of contexts within mathematical domains, or show such evidence only once.
Capable / Under the instruction of the teacher candidate, students show an ability to apply mathematics in a variety of contexts within major mathematical domains on 3 – 5 occasions.
Accomplished / Under the instruction of the teacher candidate, students show a superior ability to apply mathematics in a variety of contexts within major mathematical domains on more than 5 occasions.

Score: ______

Comments:

8. Engage students in developmentally appropriate mathematical activities and investigations that require active engagement and include mathematics-specific technology in building new knowledge. (NCTM/CAEP Standard 5b)

Beginning / Under the teacher candidate’s instruction, students are not observed engaging in developmentally appropriate mathematical activities, or investigations requiring active participation or including mathematics-specific technology, or display such evidence only once
Capable / Under the teacher candidate’s instruction, students are observed engaging in developmentally appropriate mathematical activities and investigations that require active participation and include mathematics-specific technology on 2 – 3 occasions
Accomplished / Under the teacher candidate’s instruction, students are observed engaging in developmentally appropriate mathematical activities and investigations that require active participation and include mathematics-specific technology on more than 4 occasions

Score: ______

Comments:

9. Collect, and organize diagnostic, formative, and summative assessment evidence to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction (NCTM/CAEP Standard 5c.i).

Beginning / Collection and organization of diagnostic, formative, and summative assessment evidence is spotty, or is disorganized, or in evidence only once.
Capable / Teacher candidate collects and organizes diagnostic, formative, and summative assessment evidence to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction on 3 – 5 occasions throughout their student teaching semester
Accomplished / Teacher candidate collects and organizes diagnostic, formative, and summative assessment evidence to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction on more than 5 occasions throughout their student teaching semester

Score: ______

Comments:

10. Analyze and reflect on diagnostic, formative, and summative assessment evidence and determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction (NCTM/CAEP Standard 5c.ii).

Beginning / Analyzation and reflection on diagnostic, formative, and summative assessment evidence is spotty, to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction throughout their student teaching semester, or such evidence is on display only once.
Capable / Teacher candidate analyzes and reflects on diagnostic, formative, and summative assessment evidence to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction on 3 – 5 occasions throughout their student teaching semester
Accomplished / Teacher candidate analyzes and reflects on diagnostic, formative, and summative assessment evidence to determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction on more than 5 occasions throughout their student teaching semester

Score: ______

Comments: