nctm tips for teachers - binder

8/13/2019 NCTM Tips for Teachers - Binder

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Top Ten Things I Wish I Had Known When I Started Teaching

Current Collection of Tips

These tips were highlighted both in the Activity Books (ELEM MS HS) at the AnnualMeeting and also in the New Teacher Strand.

For more highlights from the Annual Meeting, please check out the Blog and theWebCasts of se lected sessions.

The following tips are from the series Em p o w e r i n g t h e Be g in n i n g Te a ch e r i n M a t h e m a t i cs , byCynthia Thomas.

10. Not every student will be interested every minute. No matter how much experience you have orhow great you are at teaching, you w ill encounter times in the classroom when no student is interested!The solution is to change your tone of voice, move around the room, or switch from lecturing to someother activity. Maybe you can even use a manipulative to increase the students’ understanding and,possibly, their level of interest.

9. If a lesson is going badly, stop. Even if you have planned a lesson and have a clear goa l in mind, if your approach is not working—for whatever reason—stop! Regroup and start over with a differentapproach, or abandon your planned lesson entirely and go on to something else. At the end of the day,be honest with yourself as you examine what went wrong and make plans for the next day.

8. Teaching will get easier. Maybe not tomorrow or even next week, but at some point in the year, your job w ill get eas ier! Try to remember your first day in the classroom. Were you nervous? Of course; all of uswere. See how much better you are as a teacher already? By next year, you w ill be able to look back ontoday and be amazed at how much you have learned and how much easier so many aspects of teachingare!

7. You do not have to volunteer for everything. Do not feel that you always have to say yes each timeyou are asked to participate. Know your limits. Practice saying, “Thank you for thinking of me, but I do nothave the time to do a good job with another task right now.” Of course, you must accept yourresponsibility as a professional and do your fair share, but remember to be realistic about your limits.

6. Not every student or parent will love you. And you will not love every one of them, either! Thosefeelings are perfectly acceptable. We teachers are not hired to love students and the ir parents; our job isto teach students and, at times, their parents as well. Students do not need a friend who is your age;they need a facilitator, a guide, a role model for learning.

5. You cannot be creative in every lesson. In your career, you will be creative, but for those subjectsthat do not inspire you, you can turn to other resources for help. Textbooks, teaching guides, andprofessional organizations, such as NCTM, are des igned to support you in generating well-developedlessons for use in the classroom. When you do feel creative and come up with an effective and enjoyablelesson, be sure to share your ideas with other teachers, both veterans and newcomers to the profession.

4. No one can manage portfolios, projects, journals, creative writing, and student self-assessment allat the same time and stay sane! The task of assessing all these ass ignments is totally unreasonable toexpect of yourself as a beginning teacher. If you want to incorporate these types of exercises into yourteaching, pick one for this year and make it a priority in your classroom. Then, next year or even the yearafter that, when you are comfortable with the one extra assignment you picked, you can incorporateanother innovation into your teaching.

3. Some days you will cry, but the good news is, some days you will laugh! Learn to laugh with yourstudents and at yourself!

2. You will make mistakes. You cannot undo your mistakes, but berating yourself for them iscounterproductive. If the mistake requires an apology, make it and move on. No one is keeping score.

1. This is the best job on earth! Stand up straight! Hold your head high! Look people in the eye and

4/10/2011 Top Ten Things I Wish I Had Known …

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Start Student Teaching Successfully!


Realize that you are not alone. Keep in close contact with yourclassmates who are also student teaching. Share stories aboutwhat is working well and what may be frustrating you. Byexchanging your successes, you will be adding to your own "bank"of good ideas. By listening to others’ frustrations, you w ill gain thewisdom on how to avoid creating such situations in your ownclassrooms. And, by sharing your frustrations, you will gain advicefrom someone removed from the situation. Join a social networkingsite targeted toward teachers to expand your contacts. Try NCTM’sFacebook or Twitter, to start.Initiate a conversation with your cooperating teacher beforeyour assignment, if possible, about your learning preferences andexpectations. Offer to join to help decorate the room for a newsemester! Consider showcasing mathematical artwork of yourstudents, such as tessellations, or post some problems forstudents to think about. It will be helpful to exchange expectationsin advance, so that you can both be sensitive to your differences. On the other hand, be yourself!Don’t conform to who you think your supervising teacher wants you to be; rather, take advantageof the support that he or she has to offer as you mature into your own teacher.Prepare yourself by reading instructional magazines and offering lesson suggestions to yoursupervising teacher, even before you start doing the teaching yourself. This shows that you arenot only engaged in observation, but are also looking for ways to engage the students. Itdemonstrates that you are advocating for the students ’ learning by going above and beyond therequirements. For ideas, check out Illuminations, a free database of lessons and activities.Set up an observation schedule early on. Avoid a situation where the supervising teacher takesadvantage of you be ing there and leaves the room frequently. Make it clear that you value his orher constructive criticism, and that a lot of your learning depends on these conversations andreflections in addition to the teaching practice itself. Review the tips on reflection and an examplespecific to your grade.

Ask to rotate around the room and work with students as they complete assignments or workthrough problems in class as soon as you are comfortable, to he lp transition from observation toteaching. You will gain students’ trust and reduce the anxiety of solo teaching the entire class whenthe time comes.Take care of yourself! Make sure that you are getting enough rest, eating well, and exercising.Wash your hands more often, and don’t forget your vitamins. You will be subjected to more illnessin the classroom because you will be in contact with more people than you are accustomed to. Buildup your immunity before the stresses of student teaching have a chance to bring it down!Ask questions to get to know exactly what you will do when students misbehave. Doing nothingand trying to "be cool" will gain less respect than if you se t up an environment w ith clearly definedrules and consequences. Try to be consistent with other teachers’ rules. Tweak them as necessaryas you ga in experience of your own.Be early, not on time. Punctuality is very important as a student-teacher, and even more as asupervising teacher. Show your cooperating teacher that you are ready for your own classroom byarriving early to get organized and greet the students as they enter. If you arrive right on time, youare setting a bad example to the students, and w ill also be putting your supervising teacher in anawkward situation- wondering if you will be there and be prepared.Prepare a letter to introduce yourself to your students and parents in advance, if possible. Include your zea l and personal motivation for teaching, a few of your interests, and youreducational background and goals for your student teaching experience. Limit it to the front of apage. Allow your supervising teacher to edit the letter be fore mailing it out. Contacting parentsbefore they have a reason to contact you is critical to ensure a constructive relationship.Always err on the side of dressing too formally. Dressing too casually is unacceptable in theprofessional world, and you are now in it! Embrace your newest opportunity by dressing inbusiness casual wear. Especially for younger teachers, over-dressing may help set you apart andgain you respect from your students and colleagues. It is possible to be professional, comfortableand s tylish at the same time.Get to know the office and custodial staff. If there is something that you need outside of theclassroom, these will be the ones you are running to! Stop by and say “Good morning” on your

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way in. They will alert you of any happenings that day, and you w ill gain extra support that cancome in handy some days.Share your interests and capitalize in the classroom by showing off your talents! If you are anartist, select a project where your students w ill be creating mathematical works of art. If you have acraft hobby, create a mathematical construction with your class. If you are a football player, have adiscussion about the math and physics in your sport. Students will be more receptive to yourteaching as you build relationships by sharing experiences and interests – ultimately, allowingstudents to get to know you. They will be more apt to share in class dialogue if they feelcomfortable talking and don’t feel like you are judging their responses all the time.Invite the principal to watch a lesson that you are excited about. It would be great to have yoursupervising teacher AND your principal’s recommendation upon completion of student teaching; and

inviting the principal not only shows your confidence, but also gives him or her something to talkabout in your recommendation.Consider doing your first professional development activity with your supervising teacher. Besides attending those scheduled by your school or district, consider going to an NCTM conferenceto attend the New Teacher Strand, or sign up for an NCTM e-workshop or e-seminar targeted forother new and pre-service teachers.Be extremely careful when talking about students and teachers. You never know other people’srelationships to the students that you are working with. It’s great to exchange s tories aboutyour first semester in the classroom, but be careful not to say anything negative. Even when talkingabout your experiences with your college professors, it’s still a good idea to leave the students’ names out of your conversation. Don’t join in the gossip in the lounge, either. Although you mayfeel like it helps you bond with some teachers, you w ill be burning bridges w ith others. You will berespected by all if you just stay out of it.Send thank you letters to your supervising teacher, your principal, and anyone else that had animpact on your learning experience. It is important to continue the relationships as you continuethrough your teaching career. Having someone to ask a quick content or pedagogical question toand to share the stresses and successes o f teaching is important. Friends in other businesses orindustries w ill not value these as your "math teacher" friends will, so make the effort to keep them. Smile! This makes more of a difference than you can imagine. Smiles are contagious. Others willreact to you in a more pos itive way if you appear friendly and approachable! This includes yourstudents, other teachers, office staff, and even the principal.

For more reading on be ing a successful beginning teacher, check out the Empowering the BeginningTeacher series or the Mathematics for Every Student publications for your gradeband: Elementary, MiddleSchool, and High School.

Copyright © 2011, National Council of Teachers of Mathem atics.

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YOU have the power to motivate!

Don't beg, buy, or force. INVITE! Every day work to invite every student to join you in learning

math. From the way you greet them when they enter the room, to taking the time to listen tothem, to appreciating their insights and e ffort, to believing in their potential, you can invite studentsto be the most important part of the learning process. Find a copy of Inviting School Success byWilliam Purkey.Believe in your students and foster a sense of ownership. It is important that you believe andthat each student knows you believe they can be successful. When they are successful (and makesure every child feels success early) show that they are responsible for their own success. It iscritical that students believe that failure results from a lack of effort and NOT a lack of aptitude. If you want your student to persevere in similar tasks in the future, the first step is getting yourstudent to believe that with increased effort he or she CAN do it!Praise students in ways that reward effort, not ability. By praising students for effort, theyrealize that their concentration and dedication are valued. They will tend to sustain the motivationand perseverance necessary in fulfilling challenging tasks.Always listen and invite students to improve. It is easy for students to blame their failures on

lack of ability, busy schedules, and so on, but the trick is getting them to be lieve that they are INcontrol of their outcomes. Instead of punishing them for failure, try a constructive conversationabout how they could improve for next time. Work with them to create an action plan. Did they notallow for enough time? Allot time in a planner with them. Were they unclear on the directions?Encourage them to contact you before the due date to make sure they are on the right track nexttime.Model how you want your students to act. It’s contagious! You are actually more motivated tosucceed when you see someone else succeeding. Exhibit your personal excitement about yourstudents, your job and what we're learning. When you are challenged, value your mistakes aspositive learning experiences.

Teach students to set goals. Especially as you introduce a new project or

announce an upcoming exam, work with students to set realistic andmeasureable goals. A goal is a contract to oneself. Direct them to break up theirultimate goal into smaller steps, including specific times to get started. Makesure that the goals are challenging, yet attainable. Check in with your studentsoften. It will help you informally assess them and also keep them on track. Feelfree to modify this Goal Setting Handout.

Invite students to make the class their class. Encourage input and feedback often. As soon asthey realize that you truly care about their input, they will respond by showing more concern toplease you. Give them the freedom to choose the order that they complete assignments or chores,the freedom to choose an area of the classroom to work, or the freedom to select a research topicor project option.Encourage cooperation instead of competition. As educators, our main goal should be the processof learning, and not the outcome. To create cooperative learning arrangements, be sure that youractivity values effort and not only ability. Monitor the groups to ensure that each member isaccountable in the creation and the final product.Share this list of tips with parents. Motivation of children in school is most influenced by teachersand parents. Work together to raise motivated students!

For additional resources on motivation, including research articles and classroom activities, ideas,and strategies, visit the Motivation Resource Page.

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Share your success. Everyone has a favorite mathematics lesson or research project. Share this lessonwith teachers in your school that teach similar classes. By sharing lessons before the year starts, you willincrease the number of engaging activities you have for your own classroom. Consider writing up thelesson for a professional NCTM journal. Check out the writing opportunities on the web. Impress yourcolleagues, and d isplay your students’ work.

Investigate the option of an online grading program. If your district doesn't a lready use a gradingprogram, see if they have considered getting one. Such systems make it poss ible to share grades andother information via the Internet w ith students and parents. This makes for fewer parent phone calls,fewer students asking questions about their grades, less time spent preparing lists of missingass ignments, and best of all, no last-minute panic at report card time. Parents and s tudents appreciate

having instant access to what is missing and what is due. But do not get behind on grading. You expectstudents to turn work in on time, so you too, should have the courtesy to assess and return that workpromptly. You may even find yourself much more accountable when grades are posted for parents toview.


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The First Days of School and All Year Long


Become an advocate for mathematics. Celebrate the mathematics learning that is taking place in yourschool. Plan a school-wide math bulletin board, and display student work. Collaborate w ith other teachersso that each gets a turn. Share your experiences (math fairs or family nights, for example) with the localnewspaper. Letting others know about your school may result in a tremendous boost to your school’smathematics program, and ultimately more funding as well.

Take Notes. Make a place for yourself where you can jot down observations quickly throughout the day.Informal observations early in the year can be helpful further down the road if you have a student whomay have a special need or is displaying behavior that continues to disrupt the class. Also, documentwhat went we ll and what could use improvement each time you use a lesson, and more importantly, stayorganized - so that you can find and consider the notes next time around! Date each obse rvation.

Use email for parent contacts whenever possible. This saves time and makes it easy to keep a “paper” trail. Parents appreciate the ease of contact. Talk to parents early on—establish a positive relationshipbefore there a re problems. Send them a positive email about something you notice about their student.

Those positives are like money in the bank when you do encounter a discipline problem later in the year.And, from an organizational point of view, these upbeat notes encourage the practice of communicatingby email.

Keep seating charts handy. This w ill aid you in taking attendance in a split second as students arecompleting the ‘class starter’, a task written on the board to get their minds into gear. It will be the secretto knowing everyone’s names instantly. The rosters can a lso be helpful for fire drills, and are invaluablefor substitute teachers.

Take a leadership role in mathematics by offering support. Start a professional reading group todiscuss mathematics teaching and learning. Schedule a time (even lunch hour) once a month to meet withother math teachers in your school to share ideas and ask each other questions. Involving beginningteachers in a mathematics-related reading group would help everyone involved grow as a teacher.Involving veteran teachers will allow them fresh ideas and an opportunity to mentor. Consider using theseries Empowering the Beginning Teacher of Mathematics for topic ideas for the meetings.

Know your discipline/classroom management strategies. Take time to think about what is and is notacceptable in your classroom. What kinds of things are NOT okay? How are you going to handle them?Think about what kind of learning environment you would like to create for and with students. On the firstday, work as a class to set expectations for behavior and work habits. Chart, model, practice, andreinforce behavior expectations. Keep it simple; having a long list of rules may be difficult to monitor andenforce.

Ask the principal to purchase a NCTM school membership. The school membership includes asubscription to a journal, reduced registration fees for all teachers in the school at the annual meetingand regional conferences of NCTM, and 20 percent off NCTM educational materials and special products.This is a great way to strengthen the school mathematics program with access to high-quality educationalmaterials and professiona l development opportunities.

Make mathematics a priority within your classroom. Plan to integrate mathematics with other subjectareas. An easy way to get started is to collect children’s literature that promotes mathematical concepts.The April 2005 focus issue of Mathematics Teaching in the Middle School has several ideas that can bemodified for use in the lower or higher grades. Connections can also be made to your science and socialstudies curriculum by analyzing data that can be extended into a real-life problem-solving situation. Seethe tips on Using Current Events and Real Data.

Lastly, let go of the things that don’t really matter. Be conscious of what you are spending your time onas a teacher. Step back regularly and decide what tasks are producing the least gains for your studentsand eliminate them in order to make time for more worthy tasks or, equally important, time for yourself!

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Differentiated Learning


Get real. It’s impossible to look at any classroom and pretend that all students are alike.Instead, focus on the differences that exist, value the diversity, and allow each student theopportunity to shine. Teachers should be open to different approaches and strategies as longas students are able to explain their reasoning. Students want the chance to be original,resourceful, or ingenuous.

Blend whole-class, group, and individual instruction. It is more effective and efficient to usedifferent strategies in different situations. When using groups, rotate students based ondemonstrated know ledge, interest, and/or learning style preferences with the aim of moving allstudents to a higher level of achievement. Use the groups to set up learning activities that:teach new concepts, apply concepts previously learned, and a lso revisit skills not mastered.

Be proactive. Embrace accountability. You as a teacher are respons ible and obligated to plan avariety of ways to facilitate learning. Instruction may be differentiated in content, process , orproduct according to the students’ readiness, interests, or learning style. Students must be ableto express themselves in what they learn, how they learn it, and how they demonstrate theirunderstanding. As you progress as a great teacher, you will become more comfortable usingmultiple instructional strategies and a variety of representations at the same time to increasethe chances of reaching all students.

Acknowledge that students have different learning styles, learn at different speeds, are at

different comfort levels of thinking abstractly, and differ in abilities to make connections. Offerchoices and flexibility in the classroom. When appropriate, set up learning centers to providechoices. Make sure the centers include varied activities such as skill practice, problem solving,manipulatives, games, working w ith technology such as computers or calculators, graphs andother visuals, and writing opportunities. This will provide for a more comfortable, engaging, andinviting learning environment for students with different levels of understanding and differentinterests.

Never separate assessment from instruction; rather integrate assessment into instruction bymaking informal assessments a way of life in your classroom. In the classroom, focus onqualitative assessment more than quantitative assessment. It is imperative to get to know eachstudent’s achievement levels and strengths and weaknesses. Pre-assessment is a critical firststep that should be used before designing any lesson. Don’t assume what your students know

or don’t know; find out!

Get to know your students! Outside of the classroom, keep up on your students’ interests. Tryto find time to make a basketball game or a theatre production to show that you are interested inthem outside of mathematics class. In the classroom, use pe rsonal interest inventoriesregularly. Once you know your students interests, you will be able to better create ass ignmentsthat fit your students ’ interests. Students w ill be more engaged in the learning if they feel it wasdeveloped around their interests.

Use a variety of forms of assessment: formal tests, homework assignments, journals,discussions, and presentations. Equally important is that you follow through; use the results of

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.

Reflect on lessons, projects, evaluations, and everything else that goes on in your classroom.Focus on how you could modify lessons to better fit the students’ needs and interests.

Focus on the students! It may be easier for you to lecture and assign drill and practice, butremember that your ultimate goal is to be in the best interest of your students’ learning. Usemore inquiry-based teaching practices and investigations.

Realize that teaching is evolutionary. Great teaching doesn’t happen overnight. It takespatience and consistent dedication. Focus on becoming comfortable differentiating one newlesson at a time. Your plan must include more than the content. You also will need a plan formanaging time and keeping students focused. You may worry about disruptions, but in acollaborative learning environment, students will be more engaged and disruptions maydecrease. Students are unique, so the same approaches aren’t going to work year to year oreven day to day. As teachers, we must monitor each learner, their learning, and makecontinuous adjustments.

Take the time to briefly pre-teach or even re-teach to meet the needs of students beforeintroducing new content goals. Use heterogeneous groups to facilitate a tutoring and mentoring

relationship between students, but be careful not to overuse this strategy. Hold studentsaccountable for their own learning. The more skilled students deepen their understanding byarticulating concepts, and the less skilled have a chance to learn ideas from a different source.Sometimes a peer’s words are easier to internalize and may be less intimidating than workingone-on-one with the teacher.

When differentiating your classroom, don’t leave out the gifted students. Be cautious that youare assigning open-ended rich inquiry activities instead of more work or always us ing peer-tutoring and mentoring relationships. Differentiating should allow ALL students to be enriched.Differentiating is NOT adjusting the workload assigned based on ability levels or gradingdifferently based on perceptions o f students ’ capabilities.

Arrange your classroom in clusters to promote mathematical literacy. Get your studentscomfortable with the norms associated with collaborative learning; it’s a necessary prerequisiteto differentiated instruction, and it also creates more opportunities for interaction. Imagine ateacher in a classroom of 32 students. In a 50 minute class period, she can’t dedicate even twominutes to a student individually, but in groups of 4, she could dedicate more than 6 minutes to agroup. Additionally, when working with one group, the other groups would be on taskcommunicating and making progress.

Visit the NCTM Bookstore for Good Questions: Great Ways to Differentiate MathematicsInstruction. To help K–8 teachers differentiate math instruction w ith less difficulty and greater

success, this resource:Underscores the rationale for differentiating math instruction.Describes two universal, easy-to-implement strategies designed to overcome the problemsthat teachers encounter.Offers almost 300 questions and tasks that teachers and coaches can adopt immediately,adapt, or use as models to create their own.Includes Teaching Tips sidebars and an organizing template at the end of each chapter tohelp readers build new tasks and open questions.Shows how to create a more inclusive classroom learning community with mathematical talkthat engages participants from all levels

For additional resources on differentiated learning, including articles, visit the Differentiated InstructionResource Page.

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Homework

NCTM’s Tips for Teachers

Only assign what’s necessary to augment instruction. If you can get sufficient information byassigning only five problems, then don’t assign fifty.

Focus on practice and review. Give students a chance to try new material, further practice skillsthey have recently learned, and review something they already know.

Take students’ age into consideration when determining the amount of homework to ass ign.Recommendations from “Helping Your Students With Homework: A Guide for Teachers,” publishedby the U.S. Department of Education, lists the following:

Grades 1-3: up to 20 minutes a nightGrades 4-6: 20-40 minutes a nightGrades 7-9: up to 2 hours a nightGrades 10-12: 1½- 2½ hours per night

Remember, this is a cumulative amount. If you are only one of five teachers assigning homework,you should adjust accordingly.

Share a list of homework rules before handing out the first ass ignment. A written explanation of expectations will increase the likelihood that assignments are completed. Let students know thathomework is important, and that not do ing an assignment will have consequences, which mayinclude lower grades.

Let students know ahead of time when homework will be assigned. Some teachers always ass ignhomework on specific nights—every Tuesday and Thursday, for example. This lets students andparents know when to expect homework.

Designate a Homework Collector. Assign a student to gather the papers at the start of class whileyou take roll or attend to othe r administrative tasks.

Have a weekly prize drawing. Students get a ticket for each homework assignment they complete,and a t the end of the week, a winner is randomly chosen. (Plus, this activity can serve as themotivation for a probability lesson!)

Employ a “While You Were Out” form for students to fill out indicating any class periods theymissed. (Leave blank copies of this form in a location accessible to students.) When students returnthese forms, fill out the form indicating the class work, homework, or tests that students missed,and return the forms to students. When students complete the make-up work, they should attachthe form. Having a system for missed work w ill help you w ith organization, and it will reduce thenumber of last-minute assignments turned in at report-card time.

Give constructive feedback. Students are more apt to complete assignments and advance theirlearning when they get consistent and constructive feedback. Make an e ffort to provide writtencomments on student work that lets them know what they did well and what they need to improve.


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Grading


Use rubrics. Conduct a class discussion in which students develop a rubric to be used for scoringperformance tasks. This allows students to gain an understanding of expectations for solutions tomulti-step problems.Use notebook/homework quizzes as a way to easily assess if students are doing their homework.Provide students with a list of 10 homework problems to copy from their notebook (no textbooks)and you grade these problems. This also allows student more time to do homework if they getsomething they don’t understand.Create macros in a spreadsheet to make grading eas ier. See our example.Avoid all-or-nothing grading schemes. Insist on fully detailed explanations whenever yourstudents so lve problems, and reward reasonable efforts with partial credit. This encouragesstudents to value the process of solving a problem as much as the product of obtaining a correctanswer.Uses pluses, not minuses. Use positively oriented credit accumulation; that is, use “+2 out of 4points” rather than “-2 out of 4 points.” Test yourself. You should be able to complete a test in a quarter of the time that your students willhave.Be careful of “indiscriminate zeroes.” Say a student averages 96 on five ass ignments. Then failsto turn in a sixth ass ignment and is given a zero her homework average plummets to 80. Thismakes a student who normally does A-level work look like a C student.


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Exemplars® Standards-Based Math Rubric*

Problem Solving Reasoning and Proof Communication Connections Representation

Novice No strategy is chosen, or astrategy is chosen that will notlead to a solution.

Little or no evidence of en-gagement in the task present.

Arguments are made with nomathematical basis.

No correct reasoning nor justica-tion for reasoning is present.

No awareness of audience orpurpose is communicated.

orLittle or no communication ofan approach is evident

orEveryday, familiar language isused to communicate ideas.

No connections aremade.

No attempt is made toconstruct mathematicrepresentations.

Apprentice A partially correct strategy ischosen, or a correct strategyfor only solving part of thetask is chosen.

Evidence of drawing on someprevious knowledge is pres-ent, showing some relevant

engagement in the task.

Arguments are made with somemathematical basis.

Some correct reasoning or justica-tion for reasoning is present withtrial and error, or unsystematictrying of several cases.

Some awareness of audienceor purpose is communicated,and may take place in the formof paraphrasing of the task.

orSome communication of anapproach is evident throughverbal/written accounts and

explanations, use of diagramsor objects, writing, and usingmathematical symbols.

orSome formal math languageis used, and examples are pro-vided to communicate ideas.

Some attempt to re-late the task to othersubjects or to owninterests and experi-ences is made.

An attempt is made toconstruct mathematicrepresentations to re-cord and communicatproblem solving.

*Based on revised NCTM standards. © 2009, Exempla


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Exemplars® Standards-Based Math Rubric (Cont.)*

Problem Solving Reasoning and Proof Communication Connections Representation

Practitioner A correct strategy is chosen based on mathematical situa-tion in the task.

Planning or monitoring ofstrategy is evident.

Evidence of solidifying priorknowledge and applying it to

the problem solving situationis present.

Note: The practitioner mustachieve a correct answer.

Arguments are constructed withadequate mathematical basis.

A systematic approach and/or justication of correct reasoning ispresent. This may lead to...• clarication of the task.• exploration of mathematical

phenomenon.

• noting patterns, structures andregularities.

A sense of audience or pur-pose is communicated.and/orCommunication of an ap-proach is evident through amethodical, organized, coher-ent sequenced and labeledresponse.

Formal math language is usedthroughout the solution toshare and clarify ideas.

Mathematical con-nections or observa-tions are recognized.

Appropriate and ac-curate mathematicalrepresentations areconstructed and reneto solve problems orportray solutions.

Expert An efcient strategy is cho-sen and progress towards asolution is evaluated.

Adjustments in strategy, ifnecessary, are made alongthe way, and / or alternative

strategies are considered.

Evidence of analyzing thesituation in mathematicalterms, and extending priorknowledge is present.

Note: The expert mustachieve a correct answer.

Deductive arguments are used to justify decisions and may resultin formal proofs.

Evidence is used to justify andsupport decisions made andconclusions reached. This may

lead to...• testing and accepting or re- jecting of a hypothesis or conjec-ture.• explanation of phenomenon.• generalizing and extendingthe solution to other cases.

A sense of audience and pur-pose is communicated.

and/orCommunication at the Prac-titioner level is achieved, andcommunication of argumentis supported by mathemati-

cal properties.

Precise math language andsymbolic notation are usedto consolidate math thinkingand to communicate ideas.

Mathematicalconnections orobservations areused to extend thesolution.

Abstract or symbolicmathematical repre-sentations are con-structed to analyzerelationships, extendthinking, and clarifyor interpret phenom-

enon.

*Based on revised NCTM standards. © 2009, Exempla


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evel Understanding

• There is no solution, or the solutionhas no relationship to the task.

• Inappropriate concepts are appliedand/or procedures are used.

• The solution addresses none of themathematical componentspresented in the task.

• The solution is not completeindicating that parts of the problemare not understood.

• The solution addresses some, butnot all of the mathematicalcomponents presented in the task.

• The solution shows that theStudent has a broad understandingof the problem and the majorconcepts necessary for its solution.

• The solution addresses all of themathematical components

presented in the task.

• The solution shows a deepunderstanding of the problemincluding the ability to identify theappropriate mathematical conceptsand the information necessary forits solution.

• The solution completely addressesall mathematical componentspresented in the task.

• The solution puts to use theunderlying mathematical conceptsupon which the task is designed.

© Exemplars, 2006

Strategies, Reasoning, Procedures

•No evidence of a strategy or procedure, or uses astrategy that does not help solve the problem.

• No evidence of mathematical reasoning.• There were so many errors in mathematical

procedures that the problem could not be solved.

• Uses a strategy that is partially useful, leading someway toward a solution, but not to a full solutionof the problem.

• Some evidence of mathematical reasoning.• Could not completely carry out mathematical

procedures.• Some parts may be correct, but a correct answer is

not achieved.

• Uses a strategy that leads to a solution of theproblem.

• Uses effective mathematical reasoning.• Mathematical procedures used.• All parts are correct and a correct answer is

achieved.

• Uses a very efficient and sophisticated strategyleading directly to a solution.

• Employs refined and complex reasoning.• Applies procedures accurately to correctly solve the

problem and verify the results.• Verifies solution and/or evaluates the

reasonableness of the solution.• Makes mathematically relevant observations and/or

connections.

Communication

• There is no explanation of the solution, theexplanation cannot be understood or it isunrelated to the problem.

• There is no use or inappropriate use of mathemrepresentations (e.g. figures diagrams, graphs,tables, etc.).

• There is no use, or mostly inappropriate use, omathematical terminology and notation.

• There is an incomplete explanation; it maynot be clearly presented.

• There is some use of appropriate mathematicarepresentation.

• There is some use of mathematical terminologand notation appropriate of the problem.

• There is a clear explanation.• There is appropriate use of accurate mathemat

representation.• There is effective use of mathematical terminol

and notation.

• There is a clear, effective explanation detailingthe problem is solved. All of the steps are incluso that the reader does not need to infer how awhy decisions were made.

• Mathematical representation is actively used ameans of communicating ideas related to thesolution of the problem.

• There is precise and appropriate use ofmathematical terminology and notation

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Classic Exemplars Rubric


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Testing


Write the test first. Your lessons and activities should directly relate to how you assess yourstudents. Start out a new unit or chapter by writing a test that covers what you think are the maintopics, and coordinate your lessons based on the test. This way, your assessment w ill help shapehow the topics are covered, and your students may more easily see how the lessons, activities, andtest are related.

Review from the start. Provide review exercises every day to discourage “cramming.” Use warm-ups to tie together topics day-to-day and to review topics covered last week that w ill appear on anupcoming test. These review exercises w ill show you on which topics students may need extrainstruction.

Try a partner test. Divide the class into pairs, and give each partner a different version of the test.Tell your students that you w ill only grade one test from each pa ir, but don’t tell them which test it

will be. This will allow your students to talk and debate math, facilitating learning.

Try a take-home test. This w ill allow you to challenge your students w ith questions that would betoo d ifficult to answer with classroom time limitations. Encourage students to work together onsolutions outside of class.

Give ‘em a snack! Hungry students w ill focus on their empty stomachs and not the test in front of them. Even if you have a “no food” policy in your classroom, consider allowing quiet, quality snackson test days, or provide them yourself. Your students w ill appreciate the gesture and might just dobetter on the test, too!

Give every student a fair chance. All students deserve to take tests in a quiet, supportiveatmosphere. All it takes is one d isruptive student to deny them that right. Have a variety of quietactivities for early finishers to work on, and always discourage talking of any sort until all tests are

handed in.

Have students write the test. To review for a test, have small groups create sample tests withanswers. You can use some of their questions on your test.

Write helpful hints on the board. These suggestions apply to every test your students w ill take.Remind them before each test to:Read the directions first! If you don’t understand the directions, ask questions. You have to knowwhat is expected of you before you can perform.Maximize your points. Skip problems that seem time-consuming or difficult, and go back to themonce you’ve done everything else.Check your work, then turn it in. Always go over your test to fix errors.Relax! You can do this!


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Reflection Improves Instruction

Use reflection as a learning opportunity. Defuse potentially harmful moments by having studentsreflect on the ir unacceptable behavior. This forces students to think about the situation and come

to terms with why their actions were inappropriate. True interest in students' personaldevelopment will result in more respect and interest from students.

Write out your reflections for each lesson. Before a lesson, identify one or two aspects toconsider. After the lesson, ask yourself what you did well and what could be improved. Keep yourreflections organized by storing the lessons and reflections togethe r. This may mean keeping files inyour computer in the same folder as the lesson files or keeping a journal. Make sure you look backat your reflections and make the necessary improvements before teaching the same lesson,project, or unit the next time around.

Reflect on student learning. Develop a system to reflect onwhat each student is learning. Try to determine what thestudent truly comprehends. What do their eyes te ll you? Ask

questions that require critical thinking such as “What is the mostimportant part of this topic?” There may not be a right or wronganswer; however, you will be able to judge the extent of theirunderstanding. Remember, it's better to have studentsstruggling and engaged in the material than have studentscompletely removed from the lesson.

Reflect with others. Schedule informal meetings and visits w ith other teachers who teach similarcontent. Learn what others think you are doing well and how you can improve. Reflect togetherabout what “works” when teaching difficult concepts. Your students a ll have unique learning styles;

learning a variety of teaching methods is beneficial in reaching ALL students.

Create activities that allow students to reflect on their own learning. Ask all students to writeshort summaries that reflect on the "big idea." It will help them communicate their ideas moreeffectively and allow them to self-evaluate their progress. You will also benefit by assessingunderstanding outside of computational fluency.Ask for students to reflect on the class. Learn when your students are most engaged and howyou can better serve them. This should be part of a regular routine, especially when starting a newgrading period. It may be awkward for students to give constructive criticism, so be conscious toask the questions in a way that w ill yield useful feedback. Set up a feedback box so that studentscan submit anonymous feedback. Consider their needs and make changes accordingly, and you willearn the ir appreciation and respect. They will work harder for you as you become a more effectiveteacher!

Incorporate technology into the idea of reflection. Your students may be a lready spending time in

cyberspace, so take advantage of their interests and skills by asking them to blog about theirmathematical ideas. One idea is to have them post an initial response to a discussion question andrequire them to also reflect on two other students’ posts .

For additional resources on reflection, including professional development, research articles andclassroom ideas, visit the Reflection Resource Page.

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Communicating with Parents


Make the first step positive. Take note of something positive about each of your students withinthe first week of school. Then, call their parents and say, “Hi! I’m Mr./Mrs. _____, your child’steacher. Your son/daughter did _ (insert good thing here)_ in class today, and I wanted you toknow.” Follow up by telling them how to reach you if they ever have questions, and that you lookforward to meeting them and working together to he lp their child succeed.

Give parents your school phone number rather than your home phone number.

Create a separate e-mail account (Yahoo, Hotmail, and others a llow you to do this for free) for usewith school-related business. An address like [email protected] will make the addresseasy for parents to remember and for you to separate school and other e-mail.

E-mail students’ grades weekly to their parents, and maintain a web page filled with informationfor both parents and students.

Have parents e-mail you. Assign students homework to have their parent/guardian fill out aninformation form asking for contact information including an e-mail address. Award a bonus point if they also send you an e-mail with their child's name and class period in the subject line—then youcan just move the reply to the appropriate folder in your e-mail program.

Send a postcard. Have the students create the ir own mathematical collage postcard on a note card(if you put two cards together w ith the collage facing out, it runs through the laminator and comesout nicely). Then send it home with a positive comment on it sometime during the year.

Send a parent newsletter or e-newsletter to communicate the mathematical goa ls that you haveset for students and the ways in which you are helping students reach those goals.

Host a family math night. Create an opportunity for students to shine and parents to share in themathematical experiences that their children are receiving in your classroom.

Recruit parent volunteers to serve as tutors, guest speakers, and general classroom helpers.


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Tips for Tutors

Successful tutoring, like teaching, is not an exact science; it is based on thorough planning and goodcommunication between student and tutor. With continued e ffort by both, little daily frustrations are

usually outweighed by noticeable growth in the student’s mathematical competencies.

The following tips are from Guidelines for the Tutor of Mathematics, 2nd Edition.

Summary Checklist

Planning and Conducting the Early Sessions

1. Arrange a conference with the student’s instructor to determine objectives for the student tomaster.

2. Find a quiet place where you will have room to work and will be comfortable talking to the student.3. Learn why the student sought a tutor.4. Get acquainted with the student’s interests.5. Diagnose the student’s difficulties.6. Develop a positive atmosphere with the student.

Planning for the Session

1. Determine objectives for the session that are based on the student’s progress and the instructor’sguidelines. Refer to your tutoring log.

2. Review the objectives you plan to teach.3. Consult the instructor to locate resource materials and supplemental exercises.4. Construct a review activity to check on objectives that have been previously taught.5. Construct an instructional lesson for the objective(s) on the basis of suggestions from the resource

material and the instructor.6. Construct an appropriate, well-selected set of exercises for the student to complete prior to the

next tutoring session.7. Arrange for a tutoring location—one without distractions.

Conducting the Session

1. Be prompt.2. Develop a positive atmosphere.3. Sit beside the student.4. Start with a review of the objectives previously taught.5. Discuss the objective(s) for the session with the student.6. Briefly explain the new process to be introduced.7. Involve the student as soon as possible.8. When checking work, let the student make the corrections with your guidance. Avoid picking up the

pencil unnecessarily.9. Listen carefully to the student’s explanations and responses.

10. Keep your student informed about his or her progress during the session.11. Assign an appropriate set of exercises for the student to complete prior to the next tutoring

session.

12. End the tutoring session on a positive note—a success ful experience.

Following Up on the Session

1. Reflect on the tutoring sess ion by asking yourself questions about the student’s progress and yourreactions to the student.

2. Enter information on your student’s progress and learning difficulties in your tutoring log.3. Report progress and evaluation to the student’s instructor.

From Guidelines for the Tutor of Mathematics, 2nd Edition. Copyright© 1977, 2001 The National Council of Teacher of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be distributedelectronically without written permission from NCTM.

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4/10/2011 Tips for Tutors

nctm tips for teachers - binder

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