Attributes

Attributes Evidence of Achievement Teacher Actions Obstacles

Demonstrates  Perceives mathematics as a way of understanding — a view  Use entry and/or exit task  Some students who are not risk

intellectual that mathematics must make sense, and is not a sequence of  Show enthusiasm about content and takers

engagement algorithms to be memorized and applied interest in student learning  Kids can fake engagement

 Use investigations, challenge problems,  Closure

 Actively explores new ideas, posing questions about their and/or puzzle activities  Inconsistent teacher

meaning, significance, and implications  Model thought process so students have preparation; some teachers not

idea of what is involved in solving comfortable with content

 Recognizes patterns – as well as deviations – from problems; model use of meta cognition →  Discipline

previously learned patterns in data, diagrams, symbols, and check errors; include examples of  Inadequate assessment tools

words successes and common pitfalls available to actually measure

 Scaffold instruction utilizing common progress of this type

 Appreciates that abstraction and generalization are important errors to build a deeper understanding  How do you teach abstract

sources of the power of mathematics  Create safe environment for risk taking thinking to kids?; abstract

and encourage students to take risks thinking may be

 Is willing to take risks and be challenged as part of the  Consistently expect student to take risks developmentally inappropriate

learning process and make these expectations clear for some students

 Use mini-white boards to hold students  Classroom environment can be

 Contributes to and benefits from group problem-solving accountable for answering questions friend or foe

activities

 Give mandate such as, ―Turn to your  Class size

neighbor and answer this question‖  Quantity of content

 Use student work to illustrate level of  Easier to supply skill practice,

response that is expected but often need to supplement

 Have students explicitly look at and with challenge problems, etc

discuss attributes list  Lack of resources. e.g. readily

 Use pair/share and follow-up questions available quality supplements

 Utilize a reflection sheet that focuses on  Time constraints imposed by

how one learns, how one knows what they moving through entire

know, etc. curriculum

 Utilize benchmark activities to show  Need Professional

improvement over time Development that focuses on

 Common theme - make a habit cover less traditional methods, time

sheet management, juggling all the

 Use other resources, such as the internet pieces of assessment, etc

to increase interest  Difficult to keep students

 Randomly select students to share their thinking with disequilibrium

work and ideas; have students teach a without students getting too

portion of a lesson frustrated

 Summarize each day wherever you are  Reliance on how we’ve done

even if you have not completed the lesson things in the past

 100% quiz  Traditional math culture –

 Allow sufficient wait time to allow parents and kids think that

students time to think and not just respond teacher is a disseminator of

with first thing that comes to mind; do not knowledge, not a facilitator

allow students to shout out answers before

everyone has had time to think about the

question and formulate an answer

 Answer a question with a question

 Utilize collaborative groups that are

structured to require participation. e.g.

define specific roles

 Set norms for class, e.g. what does a

mathematically sound answer look like

 Put our money where our mouths are –

pick something (to start) and actually

require it and assess it regularly, e.g.

group work, student responsibility, or risk

taking

Attributes Evidence of Achievement Teacher Actions Obstacles

Takes responsibility  Attends nearly every class session and when absent, seeks  Provide homework guidelines  Some students are truly

for own learning ways to learn the material covered in class  Do not collect homework, but do not disengaged and adrift

allow students to retake assessments if  Not having self-directed

 Conscientiously prepares work assigned for class homework is not done background

 Encourage self-assessment with respect to  16-17-18 year olds

 Examines and learns from his or her errors and seeks help notation; self-check for correctness  Low reading ability in content

when needed  Outline clear expectations area

 Clarify what resources are available and  Attendance

 Takes advantage of available resources — class time, notes, encourage/require students to use them  Many times, allowing students

textbook, assignments, tutoring services, supplemental  Teach students how to use variety of to fail is not an option

materials resources available, e.g., interactive  Math anxiety

groups, share drive, web sites, and  Parental support and/or family

encourage/require students to use them issues

 Utilize college tutors  Structure of school system .

 Use "AP café" math & science support e.g., junior high students are

from peers allowed go to 9th grade with

 Promote study groups possibly using failing grades; high school

Blackboard students can make up tests

 Encourage students to seek extra help on even if missed test due to an

own. i.e., before school, during free unexcused absence

periods, after school  Students lack structure/habits

 Encourage students to use post-it notes in of learning; how do you help

textbook for quick reference students become self-directed?

 Teach student how to read their book/  Inconsistent expectations

study notes within school and within

 Make solutions manual available for department with respect to late

homework checking homework, level of

expectations used when

 Create homework center; this could

grading

include postings of homework assigned so

student is responsible to find out what was  One must be careful here –

missed when absent motivation needs to come from

teachers with goal of

 HW explanation sheet (from Millie)

eventually moving toward

 Provide access to solutions after problems internal motivation; need tools

completed; incorporate frequent checks to do so—specific

for understanding administration support, but not

 Recommend pre-readers talk to other dictate

individuals  Students can adopt a "jumping

 Encourage students to drill self on through the hoop" mentality

procedures, as needed where the students just do

 Create cognitive dissonance things to get them done and do

 Utilize concept maps to summarize not treat their assignments as

valuable learning experiences

 Rely on standards-based grading

 Hold a pizza-night-review-session

Attributes Evidence of Achievement Teacher Actions Obstacles

Perseveres when faced  Sets aside the time necessary to be successful  Use puzzles and games that require  Model trained-not having

with time-consuming extended effort; utilize NCTM problems problem solving strategies

or complex tasks  Is willing to work on problems that require time and of the day (calendar)  Lack of effort on part of

thought, particularly problems that cannot be solved by  Ask student for strategy when answering student; student shuts down

mimicking a previously seen example homework questions – What did you try? when presented with complex

Where did you get stuck? Can anyone task; apathy

 Successfully completes tasks that require organizing and give a hint without telling how to work  Students may not know

implementing multiple steps, concepts, or techniques the problem? problem solving strategies or

 Demonstrate solving smaller tasks, how to how to use them effectively

 Recognizes when an approach is unproductive and makes break the problem into parts  Authentic assessment

logical modifications to that approach or switches to another  Let students struggle (sometimes), but  One-on-one assessment

approach provide closure eventually  Whine-o-meter

 Explicit discussion about the ―okayness‖  Models

 Is convinced that effort is an important component of of struggling

 Culture issues, e.g., cell

success in mathematics  Provide students with real, engaging phones/ipods/video games

problems;

 Family issues

 Show examples of finished products that  Task completers

illustrate "bad", "good", and "excellent"

work  Limited time to allow students

time to work on challenging

 Model problem-solving process and problems

perseverance

 Low number sense skills

 Observation/conversation

 Limitation of personal

 Grade projects with a rubric and require a experiences may inhibit

problem write-up. e.g., How did you solve

understanding

the problem?, What did you find difficult?

Justify your reasoning  Frustration level of students

 Return work to students and require

resubmission until they have met standard

 Demonstrate enthusiasm

 Showcase difficult problems on

worksheets

 Do check for understanding and don't let

students move on until they get it right

 Have students check the reasonability of

their solution: Does it make sense?

Require students to solve problem with a

second method

Attributes Evidence of Achievement Teacher Actions Obstacles

Pays attention to detail  Correctly follows all parts of oral and written directions  Emphasize notational rigor  Low reading level

without needing additional reminders  Model organization and attention to detail  Many students work too fast

 Encourage self-assessment with goal of completion rather

 Makes few notational errors, e g , accidentally changing  Hold students accountable; consider use than understanding

digits, dropping or altering algebra symbols, incorrectly of partial credit and what it communicates  Lack of consistency across

positioning points on a grid, etc about the need to attend to detail grade level, across

 Student errors departments, and within

department

 Utilize a rubric type-assessment that

includes attention to detail and  Tests do not encourage this

organization of work  Negative student responses to

 Encourage, or implement strategy that reading the text, such as "It's

explicitly requires students, to read the not math" "I can't read the

math text text…you're the teacher, teach

me "

 Teach technical reading

 Hold students accountable for showing  Textbooks inadequacy with

respect to exact or approximate

units – hold the line on quizzes, tests, hw

answer

 Teach reading strategies and skills

 Lack of attention

 Scaffold notes

 Teacher may no not grade for

 Use graphic organizers detail and feel pressure to

 Use student anchors to go over assign large amount of partial

tests/answers to problems credit for work that lacks

 Encourage to read, re-read, make a details

solving plan  Confusion regarding scientific

 Give students an answer and have them notation vs mathematical

show how to get there notation