Skip to main content

Home/ eme5050/ ASSIGNMENT
John Lucyk

ASSIGNMENT - 6 views

started by John Lucyk on 29 Jan 16
  • John Lucyk
    #1 John Lucyk on 29 Jan 16
     
    Luckytoday
    Hands on Activity
    FDOE
    Educator Certification
    ________________________________________
    Certificate Lookup * Apply and Check Status

    The purpose of Florida educator certification is to support the academic achievement of our students by assuring that our educators are professionally qualified for highly effective instruction. Florida educators must be certified to teach in our public schools and in many of our private schools. Educators include classroom teachers, school administrators, and other support professionals, such as guidance counselors and media specialists. The Bureau of Educator Certification (BEC) is committed to providing timely, accurate, and efficient services to all constituents.
    New Florida Certification:
    * Out-of-state Certified Teacher or Administrator
    * Graduate of a Teacher Education Program
    * Career Changer or College Graduate of a Non-education Program
    * Foreign Trained Graduate or Non-citizen
    * High School Graduates Considering Teaching
    Florida Certified Teachers:
    * Adding a Subject or Endorsement
    * Moving from the Temporary to the Professional Certificate
    * Renewing a Florida Professional Certificate
    * Reinstating an Expired Florida Professional Certificate
    The BEC is responsible for implementing the certification provisions in Florida Statutes and State Board of Education administrative rules. These laws and rules also delegate limited certification responsibilities to Florida's school districts.
    Statutory Authority: Chapter 1012, Florida Statutes
    Rule Authority: Chapter 6A-4, Florida Administrative Code
    Rule Development for Educator Certification
    Paperless Communication: Certification Communications

    David C. LaJeunesse, Chief
    Educator Certification
    Turlington Building, Suite 201
    325 West Gaines Street
    Tallahassee, Florida 32399-0400
    U.S. Toll-Free: 800-445-6739
    Outside U.S.: 850-245-5049


    Procedural Safeguards for Exceptional Students Who Are Gifted
    6A-6.03313 Procedural Safeguards for Exceptional Students who are Gifted.
    Providing parents with information regarding their rights under this rule is critical to ensuring that they have the opportunity to be partners in the decisions regarding their children. It is also critical that local school boards provide information about these rights to appropriate district and school personnel so that the needs of the student can be identified and appropriately met. The school board's policy and procedures for procedural safeguards shall be set forth in accordance with Rule 6A-6.03411, Florida Administrative Code (F.A.C.), and shall include adequate provisions for the following:
    (1) Prior notice. The school district shall provide parents with prior written notice a reasonable time before any proposal or refusal to initiate or change the identification, evaluation, educational placement of the student or the provision of a free appropriate public education to the student.
    (a) The prior notice to the parents shall be written in language understandable to the general public and shall be provided in the native language or other mode of communication commonly used by the parent unless such communication is clearly not feasible to do so.
    (b) If the parents' mode of communication is not a written language, the school district shall ensure:

    1. That the notice is translated to the parents orally or by other means in their native language or mode of communication;
    2. That the parents understand the content of the notice; and
    3. That there is written documentation that the requirements of subparagraphs (1)(b)1. and 2. of this rule have been met.

    (c) The notice to the parents shall include:
    1. A description of the action proposed or refused by the district, an explanation of why the district proposes or refuses to take the action, and a description of any other options the district considered and the reasons why those options were rejected;
    2. A description of each evaluation procedure, test, record, or report the district used as a basis for the proposed or refused action;
    3. A description of any other factors that are relevant to the district's proposal or refusal; and
    4. Information on how the parent can obtain a copy of the procedural safeguards specified in this rule.

    1
    (2) Content and Provision of the Procedural Safeguards to Parents.
    (a) Parents must be provided a copy of their procedural safeguards which provides a full explanation of the provisions included in this rule.
    (b) A copy of the procedural safeguards must be available to the parents of a child who is gifted, and must be given to the parents, at a minimum:

    1. Upon initial referral for evaluation;
    2. Upon refusal of a parent's request to conduct an initial evaluation;
    3. Upon notification of each EP meeting; and
    4. Upon receipt of a request for a due process hearing by either the school district or the parent in accordance with subsection (7) of this rule.

    (3) Informed parental consent.
    (a) Parents shall be fully informed of all information relevant to the action for which consent is sought in their native language or other mode of communication unless such communication is clearly not feasible.
    (b) Written parental consent shall be obtained prior to conducting an initial evaluation to determine eligibility and prior to initial provision of services to students who are gifted.
    (c) School districts shall document the attempts to secure consent from the parent as required by paragraph (3)(b) of this rule.
    (d) Parental consent is voluntary and may be revoked at any time before the action occurs.
    (e) Except for formal, individual evaluation and the initial provision of services to the student, consent may not be required as a condition of any other benefit to the parent or child. Any proposal or refusal to initiate or change the identification, evaluation, or educational placement or the provision of a free appropriate public education to the student after the initial placement is not subject to parental consent but is subject to prior notice as defined by subsection (1) of this rule.
    (f) Parental consent is not required before:

    1. Reviewing existing data as part of an evaluation; or,
    2. Administering a test or other evaluation that is administered to all students unless, before administration of that test or evaluation, consent is required of parents of all children.

    2
    (4) Parents' opportunity to examine records and participate in meetings.
    (a) The parents of students who are gifted shall be afforded, in accordance with Rule 6A1.0955, F.A.C., Section 1002.22, Florida Statutes (F.S.), and this rule, an opportunity to inspect and review their child's educational records.
    (b) The right to inspect and review education records under this rule includes the right to have a representative of the parent inspect and review the records including all records related to the identification, evaluation, and educational placement of the child and the provision of a free appropriate public education to the child.
    (c) The parents of a student who is gifted must be afforded an opportunity to participate in meetings with respect to the development of their child's educational plan.
    (5) Evaluations obtained at private expense. If the parent obtains an independent evaluation at private expense which meets the requirements of subsection (4) of Rule 6A-6.0331, F.A.C., the results of the evaluation must be considered by the school district in any decision made with the respect to the determination of eligibility for exceptional student education services.
    (a) The results of such evaluation may be presented as evidence at any hearing authorized under subsection (7) of this rule.
    (b) If an administrative law judge requests an independent educational evaluation as part of a hearing, the cost of the evaluation must be at public expense, as defined in paragraph (7)(c) of Rule 6A-6.03411, F.A.C.
    (6) State Complaint Procedures. The Department of Education shall provide parents and other interested persons the opportunity to resolve allegations that a school district has violated state requirements regarding the education of students who are gifted through the establishment of state complaint procedures.
    (a) Within ninety (90) calendar days after a complaint is filed, under the provisions of this rule, the Department of Education shall:

    1. Carry out an independent on-site investigation, if the Department of Education determines that to be necessary;
    2. Give the complainant the opportunity to submit additional information, either orally or in writing, about the allegations in the complaint;
    3. Review all relevant information and make an independent determination as to whether the school district is violating a state requirement regarding the education of students who are gifted;
    4. Issue a written decision on the complaint that addresses each issue presented in the complaint and contains findings of fact, conclusions, and the reason(s) for the Department of Education's final decision; and

    3

    1. Extend the time limit established in paragraph (6)(a) of this rule if exceptional circumstances exist with respect to a particular complaint.

    (b) Procedures for the effective implementation of the Department of Education's final decision include the following:
    1. Technical assistance activities;
    2. Negotiations; and,
    3. Corrective actions to achieve compliance.

    (c) Relationship to due process hearings.
    1. If a written complaint is received that is also the subject of a due process hearing requested pursuant to subsection (7) of this rule, or the complaint contains multiple issues, of which one or more are part of that hearing, the Department of Education shall set aside any part of the complaint that is being addressed in the due process hearing until the conclusion of the hearing. However, any issue in the complaint that is not a part of the due process action must be resolved in compliance with the procedures described in subsection (6) of this rule.
    2. If an issue is raised in a complaint filed under this subsection that has previously been decided in a due process hearing involving the same parties, the administrative law judge's decision is binding and the Department of Education shall inform the complainant to that effect.
    3. The Department of Education shall resolve any complaint that alleges that a school district has failed to implement a due process hearing decision.

    (7) Due process hearings. Due process hearings shall be available to parents of students who are gifted and to school districts to resolve matters related to the identification, evaluation, or educational placement of the student or the provision of a free appropriate public education.
    (a) Such hearings may be initiated by a parent or a school district on the proposal or refusal to initiate or change the identification, evaluation, or educational placement of the student or the provision of a free appropriate public education to the student.
    (b) A hearing shall be conducted by an administrative law judge from the Division of Administrative Hearings, Department of Management Services, on behalf of the Department of Education.
    (c) An administrative law judge (ALJ) shall use subsection (7) of this rule for any such hearings and shall conduct such hearings in accordance with the Uniform Rules for Administrative Proceedings, Chapter 28-106, F.A.C., as deemed appropriate by the ALJ including, but not limited to: the authority of a party to request a pre-hearing conference, the authority of the ALJ to issue subpoenas to compel the attendance of witnesses and the production of records, and the authority of the ALJ to issue summary rulings in absence of a disputed issue of material fact.
    (d) Status of student during proceedings.

    4
    FDOE
    1. During the time that an administrative or subsequent judicial proceeding regarding a due process hearing is pending, unless the district and the parent of the student agree otherwise, the student involved in the proceeding must remain in the present educational assignment. If the proceeding involves an application for an initial admission to public school, the student, with the consent of the parent, must be placed in a public school program until the completion of all proceedings.
    2. If the administrative law judge agrees with the parent and finds that a change of placement is appropriate, that placement becomes the agreed-upon placement during the pendency of the appeal.

    (e) Hearing rights for all parties.
    1. Any party to a hearing conducted pursuant to subsection (7) of this rule has the right:
    a. To be represented by counsel or to be represented by a qualified representative under the qualifications and standards set forth in Rules 28-106.106 and 28-106.107, F.A.C., or to be accompanied and advised by individuals with special knowledge or training with respect to the problems of students who are gifted, or any combination of the above;
    b. To present evidence, and to confront, cross-examine, and compel the attendance of witnesses;
    c. To prohibit the introduction of any evidence at the hearing that has not been disclosed to that party at least five (5) business days before the hearing;
    d. To obtain written, or at the option of the parents, electronic, verbatim record of the hearing at no cost to the parents; and
    e. To obtain written, or at the option of the parents, electronic findings of fact and decisions at no cost to the parents.

    2. Additional disclosure of information.
    a. At least five (5) business days prior to a hearing conducted pursuant to subsection (7) of this rule, each party shall disclose to all other parties all evaluations completed by that date and recommendations based on the offering party's evaluations that the party intends to use at the hearing.
    b. An administrative law judge may bar any party that fails to comply with subparagraph (7)(e)2. of this rule from introducing the relevant evaluation or recommendation at the hearing without the consent of the other party.

    5
    (f) Parental rights at hearings. Parents involved in hearings must be given, in addition to the rights described in paragraph (7)(e) of this rule, the right to:
    1. Have their child who is the subject of the hearing present; and
    2. Open the hearing to the public.

    (g) Duties and responsibilities of the superintendent or designee shall include:
    1. Implementing procedures that require the parent of a child who is gifted, or the attorney representing the child, to provide notice to the school district. The notice required, which must remain confidential, must include: the name of the child; the address of the residence of the child; the name of the school the child is attending; a description of the nature of the problem relating to the proposed or refused initiation or change, including facts relating to the problem; and, a proposed resolution of the problem to the extent known and available to the parents at the time. However, the school district may not deny or delay a parent's right to a due process hearing for failure to provide this notice.
    2. Immediately forwarding the Division of Administrative Hearings by facsimile transmission of the parent's request for a hearing upon its receipt;
    3. Notifying all parties regarding their rights and responsibilities before, during, and after the hearing. This notice should include information to the parent of any free or low cost legal and other relevant services, which are available, if the parent requests this information or if the parent or school district initiates a hearing.
    4. Determining whether an interpreter is needed and arranging for the interpreter as required;
    5. Complying with the administrative law judge's rulings regarding requests for and exchanges of evidence; discovery; the filing of motions and, scheduling, so as to meet the requirements of this rule, and the deadlines established herein.
    6. Arranging for the provision and payment of clerical assistance, the hearing, use of facilities, and a verbatim transcript of the hearing;
    7. Completing other responsibilities specified by the school board.

    (h) Duties and responsibilities of the Department of Education shall include:
    1. Maintaining a list of persons who serve as administrative law judges including a statement of the qualifications of each of these persons; and,
    2. Maintaining an index of the final orders of such hearings and providing this information to the public upon request.

    (i) Duties and responsibilities of an administrative law judge shall be:
    6

    1. To establish the date, time, and location of the hearing and any pre-hearing conference calls and motion hearings. Each hearing involving oral arguments must be conducted at a time and place that is reasonably convenient to the parents and their child;
    2. To conduct the hearing in a fair and impartial manner;
    3. To ensure that all discovery, motion practice, and pre-hearing procedures are conducted in an expedited manner, consistent with the deadlines established by this rule concerning the exchange of evidence and the issuance of the final decision.
    4. To determine if the parent wants an electronic or written copy of the final decision and the administrative record of the hearing;
    5. To determine whether the parent wants the hearing open to the public and whether the parent wants their child to attend the hearing;
    6. To determine whether the parent's advisor or representative is sufficiently knowledgeable about or trained regarding students who are gifted;
    7. To determine how evidence may be exchanged prior to and during the hearing;
    8. To determine how witnesses may be compelled to attend, be cross-examined, and confronted during discovery and at the hearing;
    9. To determine how evaluations and recommendations may be disclosed prior to and during a hearing;
    10. To summarize the facts and findings of the case and to arrive at an impartial decision based solely on information presented during the hearing;
    11. To reach a final decision and mail to all parties copies of the facts, findings and decision regarding the hearing within forty-five (45) days of the district's receipt of the parent's request or the filing of the district's request for a hearing, whichever is sooner;
    12. To be accountable for compliance with all deadlines and procedures established by the statutes and rules for such hearings;
    13. To maintain the confidentiality of all information; and
    14. To rule on requests for specific extensions of time beyond the periods set forth in subsection

    (7) of this rule, at the request of either party.
    (j) Civil action. A decision made in a hearing conducted under subsection (7) of this rule shall be final, unless, within thirty (30) days, a party aggrieved by the decision brings a civil action in state circuit court without regard to the amount in controversy, as provided in Section 1003.57(5), F.S. The state circuit court shall: receive the records of the administrative proceedings; hear, as appropriate, additional evidence at the request of a party; and, basing its decision on the preponderance of the evidence, shall grant the relief it determines appropriate. In the alternative, any party aggrieved by the administrative law judge's decision shall have the right to request an impartial review by the appropriate district court of appeal as provided by Sections 120.68 and 1003.57(5), F.S.
    7
    Specific Authority 1001.02(1)(2)(n), 1003.01(3)(a)(b), 1003.57(5) F.S. Law Implemented 1001.42(4)(l) 1003.01(3)(a)(b) , 1003.57(5), 1001.03(8) F.S. History - New 9-20-2004.
    This pamphlet helps parents of children in Florida's school districts understand the rights that go along with programs for students who are gifted. It summarizes federal and state laws on how your rights must be protected relating to notice, consent, independent educational evaluation, records, hearings, and appeals. These procedural safeguards apply for children who are gifted.
    Florida Department of Education
    Dr. Tony Bennett, Commissioner
    ESE 310581 8

    Lesson Plan


    To view this email as a web page, go here.




    Grab Your Lab Coats!
    Students become food scientists in this new K-5 interactive on RecipeForInnovation.com!


    Chobani and Discovery Education are excited to introduce students to a brand new interactive for K-5 classrooms. This unique interactive will give each student an unforgettable experience as they explore what makes up the foods they eat. The interactive introduces students to the ingredients found in dairy foods, as well how those ingredients and nutrients impact our bodies.

    Students exploring this resource will play the role of food scientist to gain an understanding of why and how dairy contributes to their health. To transform your students into food scientists researching the ingredients and nutrients in the food we eat, visit us at RecipeforInnovation.com.











    Mathematics Professor at UCF





    Bray, W.S. (2013). How to leverage the potential of mathematical errors. Teaching Children Mathematics, 19 (7), 424-431.
    How to Leverage the Potential of Mathematical Errors
    Author(s): Wendy S. Bray
    Source: Teaching Children Mathematics, Vol. 19, No. 7 (March 2013), pp. 424-431 Published by: National Council of Teachers of Mathematics
    Stable URL: http://www.jstor.org/stable/10.5951/teacchilmath.19.7.0424 Accessed: 29-01-2016 05:23 UTC

    Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp

    JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
    This content do 3 on Fri, 29 Jan 2016 05:23:09 UTC
    3 on Fri, 29 Jan 201
    ll use subject to JSTOR Terms and Conditions




    to Leverage
    the Potential of
    Mathematical
    EIncorporrating arfocus oon students'rmistakses into
    your instruction can advance their understanding.



    By Wendy S. Bray

    elling children that they can learn from their mistakes is common practice. Yet research indicates that many teachers in the United States

    limit public attention to errors during math- ematics lessons (Bray 2011; Santagata 2005). Some believe that drawing attention to errors publicly may embarrass error makers or may be confusing to struggling learners. However, exploratory research suggests that focus- ing on errors can lead to increased student engagement among struggling learners (Bray



    2007). In general, the strategy of publicly ana- lyzing and discussing mathematical errors is thought to promote conceptual understand- ing (Borasi 1994; Kazemi and Stipek 2001).
    This article explores the potential of using errors to advance students' mathematical understanding and presents a framework for infusing a focus on errors into mathematics instruction. The classroom example that fol- lows will anchor the rest of the article. Third graders who were studying initial fraction concepts received this task (see fi 1). Before






    Vol. 19, No. 7 | teaching children mathematics * March 2013 425
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions




    reading further, examine the student solutions presented in figure 2, and consider how the various solutions-correct and flawed-might be used instructionally to develop fraction concepts.

    using the framework
    The balance of this article elaborates how to design and implement lessons to leverage the instructional potential of errors. The framework has been developed through study of other teachers' handling of students' mathematical errors (Bray 2011; Santagata and Bray 2011) and attempts within my own mathematics teaching to incorporate errors. Errors can and do surface in all kinds of mathematics lessons; however, lessons designed to provoke and address stu- dents' misconceptions have a greater likelihood of making productive use of errors. Mathemati- cal tasks can be selected for their potential to expose misconceptions, and provision can be made for explicitly attending to errors during instruction.

    Selecting mathematical tasks
    Problem-based tasks that probe students' depth of understanding of mathematical ideas are use- ful for bringing students' misconceptions to the surface. Such tasks can usually be approached in different ways and often require students to justify their mathematical thinking. Tasks that are intentionally designed with contexts and numbers that provoke commonly held mis- conceptions are particularly good at revealing misunderstanding.
    In the Three Children Sharing Two Brownies task, the mathematical emphasis is on partition- ing brownies into equal parts and identifying the fractions that describe the parts. As children begin to learn about fractions, they tend to think about thirds as three parts rather than three equal parts. Consequently, students commonly devise solutions to this task with fractional parts incorrectly labeled, allowing an opportunity to explore this misconception. This task also provokes misconceptions by using numbers that yield a focus on thirds rather than the more easily represented halves or fourths. Finally, the problem context aids in allowing misconcep- tions to surface by requiring students to draw representations and devise multiple solutions.

    Planning for instruction
    After selecting mathematical tasks, anticipating the flawed ways that students will approach the tasks is a critical step for leveraging the potential of errors. A teacher can consider in advance how to use particular errors to support the mathematical agenda. With the Sharing Brown- ies task, the teacher wanted to emphasize how fractional parts are named in relation to their wholes. She anticipated that students would produce solutions with fractional parts named incorrectly and that analysis and discussion of these flawed solutions could promote students' understanding.
    As this example suggests, a lesson designed to maximize the instructional potential of errors must make provision for students to analyze and discuss flawed solutions in relation to task speci- fications and mathematical ideas. A good first step is to have students justify whether a given solution is correct. Further analysis may involve considering the logic behind an error and deter- mining how to revise and correct it.
    Flawed solutions that are selected for public

    426 March 2013 * teaching children mathematics | Vol. 19, No. 7 www.nctm.org
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions


    discussion can come from the class or from the teacher. Students' initial analysis of an error can occur independently, between partners, in small groups, or through whole-class discus- sion. However, two essentials elements are that (1) students actively engage in attempts to


    The Sharing Two Brownies task uses numbers that focus on thirds rather than halves or fourths. Requiring students to draw representations, devise multiple solutions, and label fractional parts, the task often exposes misconceptions.


    unpack the mathematics underlying the errors and (2) the teacher facilitates public discussion


    Solution A

    Solution B
    2 2

    During the planning stage, therefore, identify how examining specific errors will illuminate the mathematical agenda and make provision

    1 3 1 3

    1 1 1 1 2



    for students to grapple with errors as a com- munity of learners. Last, to inform public dis- cussion, have a plan for determining the fl ed (and correct) ways that students are approach- ing tasks (Smith and Stein 2011).

    3+ 3
    Solution C

    3+ 3= 3
    Solution D

    Implementing the lesson
    After planning a lesson with a focus on errors, 1 1 1 1



    the challenge for teachers is to make on-the- spot adjustments to the lesson in response to the actual understandings and misunderstand- ings he or she observes. To use errors effectively, teachers can take specific actions as students work on tasks and publicly discuss solutions.
    While the third graders began working on

    2+ 3
    Solution E

    3+ 3
    Solution F


    the Sharing Brownies task, the teacher cir- 2 1 1


    culated around the room to ensure that all students understood and were attempting the task. Simultaneously, she sought to gauge how students' solutions compared with what she had anticipated. After most students had two solutions, the teacher directed table groups to share their work with attention to the following questions:

    * What different solutions did your table generate?
    * Does each solution show a fair way for three children to share two brownies?
    * Did you use fractions correctly to name parts of the brownies?

    As the teacher visited table groups, she listened to students' reasoning with particular atten- tion to errors and underlying misconceptions. She also decided on the solutions-correct and fl ed-to include in a public discussion and settled on a plan for how to use these solutions to emphasize part-whole fraction relationships. Then she requested that particular solutions be


    3

    re-created on small white boards for sharing in a public discussion.
    By the time the teacher had distributed white boards, table groups often had identifi either their errors or their uncertainty about the cor- rectness of particular solutions. The teacher praised students for these observations and, if she wanted an error to be shared publicly, sug- gested that discussion of the solution could help the class better understand fractions. She also sought the permission of error makers to share their solutions publicly.

    Discussing the solutions publicly
    The public discussion of the Sharing Brown- ies task was organized in two parts. First, the teacher had the class examine solution C (see fi 2) because she had noticed that many stu- dents initially split the two brownies in half and then struggled to make fair shares. Solution C

    4+ 4

    www.nctm.org Vol. 19, No. 7 | teaching children mathematics * March 2013 427
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions



    successfully makes fair shares by partitioning the two brownies into halves and then parti- tioning one-half of a brownie into three equal parts. But then the solution incorrectly identi- fies the small parts as thirds rather than sixths. The teacher viewed this error as an opportunity to have students think deeply about how frac- tional parts are named. Specifically, she wanted students to see that they could determine the fractional amount of a part by filling the whole with parts of the same size and shape (see fig. 3). The teacher first asked Amy-the error maker-to explain her solution C to the class. Before Amy began, the teacher directed the rest of the students to listen to Amy's explanation to understand her approach and evaluate her solu- tion. Amy recounted her strategy and explained
    that she split the last half into thirds.

    The teacher asked the class to show thumbs up or down on whether Amy's strategy led to fair shares. Observing a roomful of quick thumbs up, she continued, "In this solution, are frac- tions used correctly to name parts of brownies?" Students were more hesitant with this question and displayed thumbs up, down, and sideways (i.e., unsure). After several students shared their reasoning, the teacher guided the class to agree that the one-half piece of the second brownie

    was in thirds but that one-third did not describe the fractional part of a whole brownie repre- sented by each small piece. Next, the teacher challenged students to work with their shoulder partners to figure out the fractional part of a brownie represented by each small piece. To encourage strategic thinking, she reminded students that they knew the one-half-size piece was one-half because they could fit two of them into a whole brownie, and she wondered aloud how many of the small pieces could fit into a whole brownie. After a few minutes, this part of the discussion concluded with two partnerships explaining how they determined the small piece was one-sixth of a brownie by using filling strat- egies. As students shared, the teacher directly engaged those who still seemed confused by asking them to restate why the small part was one-sixth of a brownie.
    To open the second part of the public discus- sion, the teacher displayed the white boards detailing solutions A, B, D, and E and asked the class to identify similarities. Students noted that these solutions all involved cutting brownies in three parts and that they all showed either one-third plus one-third, or two-thirds (which the class recognized as equivalent). The teacher then directed students to talk with their shoul- der partner about the following questions:

    * Which solutions show brownies split into thirds? How do you know?
    * For the solutions that do not show thirds, what fractions are they showing?

    When public discussion reconvened, students quickly identified with appropriate justification that solutions A and E showed brownies split into thirds and that solution D did not. Students were also able to use the filling strategy to justify that solution D brownies were partitioned into one-half, one-fourth, and one-fourth.
    At this point, most students were still unsure of the correctness of solution B. One partner- ship, however, used a picture to justify that the brownie was not in thirds (see fig. 4). Victoria said, "This [triangle-shaped] piece is one- fourth because you can make it four times in the square. These two [trapezoid-shaped parts] are bigger than one-fourth." Victoria and her partner had not yet determined the fractional name for the trapezoid-shaped parts, but they

    ?







    428 March 2013 * teaching children mathematics | Vol. 19, No. 7 www.nctm.org
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions



    had determined that the trapezoids could not be iterated to fi the whole. After having mul- tiple students summarize their understanding of Victoria's explanation, the teacher challenged the class to fi e out how they might add addi- tional lines to Victoria's picture to help discover the fraction of a brownie represented by the trapezoid-shaped part. Students again worked with shoulder partners and then discussed their strategies as a class.

    Focusing on the math concepts
    During the public discussion phase, two tenets can be used to guide working with errors. First, it is important to keep the focus of discussion on the conceptual underpinnings and key math- ematical lesson of a given error. To accomplish this, the teacher must be clear in her own mind about the mathematical concepts or strategies to emphasize and the trajectory along which those understandings are expected to develop. With the Sharing Brownies task, the focus was on developing students' capacity to determine and justify fractions that named specifi parts of a whole. In the public discussion, students were first led to think about flawed solutions C and D, for which the fractional parts could be justifi using the fi strategy. Then they were challenged to consider the more diffi
    fl ed solution B, for which the fractions could not be determined without partitioning the fi - ure further.
    To keep the emphasis on mathematical con- cepts, students were challenged to justify why certain aspects of the solutions were correct or incorrect. When it makes sense, students can also be guided to revise and correct fl ed solu- tions in ways that retain aspects of the original strategy. Finally, the teacher can summarize students' ideas to ensure that they connect explicitly to her mathematical agenda for the discussion.

    Fostering a community of learners
    The second principle is a commitment to having students interact with errors during public discussion as a community of learn- ers. In a community of learners, students actively engage in working collaboratively to grapple with mathematical ideas. To foster such an approach during discussions of fl ed solutions, teachers must avoid immediately

    identifying errors and instead orchestrate discussion such that students uncover and unpack errors. As students engage with errors, maintaining a classroom culture that values learning from mistakes and honors error makers is imperative.
    Sustaining active student engagement is also essential. One strategy is to explicitly assign students a job to guide their examination of errors. Students might be directed to compare, to evaluate, to develop questions, or to explain. In the Sharing Brownies lesson, the teacher fi assigned students the job of listening to Amy's flawed solution to understand and evaluate



    www.nctm.org Vol. 19, No. 7 | teaching children mathematics * March 2013 429
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions


    Phase Strategies
    Selecting mathematical tasks identify the mathematical focus and related misconceptions.
    Use problem-based tasks that emphasize the mathematical focus.
    tweak task features (contexts, numbers) to provoke misconceptions.
    Planning for instruction anticipate students' errors and identify underlying misconceptions.
    Consider how errors can be used instructionally to illuminate mathematical ideas.
    Plan a way to find out how students are approaching tasks.
    Make provision for students to analyze and publicly discuss flawed solutions.
    as students work on tasks Promote a culture of intellectual risk taking.
    Find out how students are approaching tasks and the errors they are making.
    Decide on a plan for public discussion (solutions to include, order, purpose).
    During public discussion engage students as a community of learners to analyze flawed solutions.
    emphasize the conceptual lessons of errors.
    Honor error makers and learning from mistakes.

    its accuracy. Later she gave students the job of working with a shoulder partner to determine the fractions represented in Amy's solution. The expectation of active engagement and the explicit direction on how to engage both seem highly related to the degree to which students attempt the hard work of analyzing and learning from errors.

    getting started with errors
    When planning for and teaching lessons with a focus on errors, concentrate on four phases of the process: First, select mathematical tasks for their potential to expose students' misconcep- tions. Then plan lessons with a consideration of how errors might be used to advance students' mathematical understanding. As students work, be attentive to their solutions and make a plan for incorporating errors into public discussion.


    Finally, engage students as a community of learners to analyze and revise errors such that key mathematical concepts are illuminated. (See the summary of strategies in table 1.)
    Undergirding the successful use of students' errors to promote learning is a classroom envi- ronment in which children feel safe sharing their (sometimes flawed) mathematical ideas and solutions. For children to undertake this kind of intellectual risk taking, it is essential to establish and maintain a climate of respect and supportiveness in the classroom. (See Chapin, O'Connor, and Anderson 2009 for a detailed description of how to establish and maintain these and other classroom norms that support productive mathematical discourse.) To spe- cifically prepare students for learning through examination of errors, talk with students about how mistakes are a natural and important part of the learning process. For instance, the only way to learn how to hit a baseball is by taking swing after swing and making adjustments based on what is learned from the hits and misses. In a school context, we learn to read by persisting through our diffi decoding text and learning from them.
    In addition to helping students view the examination of errors in a positive light, have explicit conversations about how to engage respectfully in discussing a classmate's flawed work. One possibility for initially working on this skill is for the teacher to present a fl ed solu- tion and say, "This is one way that I have seen children solve this problem." As students pub- licly examine the fl ed solution, prompt them to refl on appropriate ways to convey ideas.
    When asking children to share their fl ed solutions, take additional steps to respect and honor error makers. Error makers are less likely to feel put on the spot if they are aware that their solutions may contain errors and if they have some control over the process of their work being shared. Students can gain awareness of errors through informal comparison of solu- tions with peers. Teachers can give error makers control by asking permission to include their work in public discussion and by giving them a choice about whether to personally explain their mathematical approach. Some students are reluctant to talk publicly about their work if they suspect it is flawed but are happy to have the class analyze and revise their flawed

    430 March 2013 * teaching children mathematics | Vol. 19, No. 7 www.nctm.org
    This content downloaded from 132.170.193.73 on Fri, 29 Jan 2016 05:23:09 UTC All use subject to JSTOR Terms and Conditions

    Vol. 19, No. 7 | teaching children mathematics * March 2013 431
    from mistakes a more explicit and valued part of
    mathematics instruction.

    REFERENCES
    Borasi, Raffaella. 1994. "Capitalizing on Errors as 'Springboards for Inquiry': A Teaching experiment." Journal for Research in
    Mathematics Education 25 (March): 166-208.
    Bray, Wendy S. 2007. A Study of Teacher transitions to a Reform-based Mathematics Curriculum in an Urban School: The Inter- action of Beliefs, Knowledge, and Classroom Practices. PhD diss. Dissertation Abstracts International 68:11.
    Bray, Wendy S. 2011. "A Collective Case Study of the influence of teachers' beliefs and
    Knowledge on Error-Handling Practices during Class Discussion of Mathematics." Journal
    for Research in Mathematics Education 42 (January): 2-38.
    Chapin, Suzanne H., Catherine O'Connor, and Nancy Canayan Anderson. 2009. Classroom Discussions: Using Math Talk to Help Students Learn. 4th ed. Sausalito, CA: Math Solutions.
    Kazemi, Elham, and Deborah Stipek. 2001. "Pro- moting Conceptual Thinking in Four Upper- Elementary Mathematics Classrooms." The Elementary School Journal 102 (1): 59-80.
    Santagata, Rossella. 2005. "Practices and Beliefs in Mistake-Handling Activities: A Video Study of Italian and U.S. Mathematics Lessons." Teaching and Teacher Education 21 (5):
    491-508.
    Santagata, Rossella, and Wendy Bray. 2011.
    Integrating Cultural Awareness and Innovative Practices for Mathematics teacher Professional Development: A Video-Based Project Focused on Student Mistakes. Poster session presented at the Jean Piaget Society Annual Meeting, Berkeley, CA.
    Smith, Margaret S, and Mary Kay Stein. 2011.
    5 Practices for Orchestrating Productive Mathematical Discussions. Reston, Va: National Council of Teachers of Mathematics.

    Wendy S. Bray, wendy.bray@ucf.edu,
    is a former classroom teacher who is
    currently a mathematics education
    instructor for the University of Central
    Florida in Orlando. She is interested in
    detailing instructional practices that foster deep
    conceptual understanding of mathematics.
    solutions. Teachers can further honor error mak-

    ers by recognizing the logic inherent in their flawed mathematical thinking and by emphasiz- ing that their mistakes provide an opportunity for the class to better understand mathematics.

    benefiting from the framework
    As teachers begin to think about mathematics instruction with a focus on misconceptions, they become better able to anticipate students' errors and respond to them in mathemati- cally productive ways. For students, placing an emphasis on learning from mistakes correlates to participation in mathematical discourse that is more evenly distributed, as well as to greater understanding of mathematics. One teacher commented,

    When I include [an analysis of ] wrong answers, there is a place for everyone in the discussion, especially the students who don't quite get it.

    My hope is that this framework can help more teachers think about how to make learning


    Procedural Safeguards for Exceptional Students Who Are Gifted
    6A-6.03313 Procedural Safeguards for Exceptional Students who are Gifted.
    Providing parents with information regarding their rights under this rule is critical to ensuring that they have the opportunity to be partners in the decisions regarding their children. It is also critical that local school boards provide information about these rights to appropriate district and school personnel so that the needs of the student can be identified and appropriately met. The school board's policy and procedures for procedural safeguards shall be set forth in accordance with Rule 6A-6.03411, Florida Administrative Code (F.A.C.), and shall include adequate provisions for the following:
    (1) Prior notice. The school district shall provide parents with prior written notice a reasonable time before any proposal or refusal to initiate or change the identification, evaluation, educational placement of the student or the provision of a free appropriate public education to the student.
    (a) The prior notice to the parents shall be written in language understandable to the general public and shall be provided in the native language or other mode of communication commonly used by the parent unless such communication is clearly not feasible to do so.
    (b) If the parents' mode of communication is not a written language, the school district shall ensure:

    1. That the notice is translated to the parents orally or by other means in their native language or mode of communication;
    2. That the parents understand the content of the notice; and
    3. That there is written documentation that the requirements of subparagraphs (1)(b)1. and 2. of this rule have been met.

    (c) The notice to the parents shall include:
    1. A description of the action proposed or refused by the district, an explanation of why the district proposes or refuses to take the action, and a description of any other options the district considered and the reasons why those options were rejected;
    2. A description of each evaluation procedure, test, record, or report the district used as a basis for the proposed or refused action;
    3. A description of any other factors that are relevant to the district's proposal or refusal; and
    4. Information on how the parent can obtain a copy of the procedural safeguards specified in this rule.

    1
    (2) Content and Provision of the Procedural Safeguards to Parents.
    (a) Parents must be provided a copy of their procedural safeguards which provides a full explanation of the provisions included in this rule.
    (b) A copy of the procedural safeguards must be available to the parents of a child who is gifted, and must be given to the parents, at a minimum:

    1. Upon initial referral for evaluation;
    2. Upon refusal of a parent's request to conduct an initial evaluation;
    3. Upon notification of each EP meeting; and
    4. Upon receipt of a request for a due process hearing by either the school district or the parent in accordance with subsection (7) of this rule.

    (3) Informed parental consent.
    (a) Parents shall be fully informed of all information relevant to the action for which consent is sought in their native language or other mode of communication unless such communication is clearly not feasible.
    (b) Written parental consent shall be obtained prior to conducting an initial evaluation to determine eligibility and prior to initial provision of services to students who are gifted.
    (c) School districts shall document the attempts to secure consent from the parent as required by paragraph (3)(b) of this rule.
    (d) Parental consent is voluntary and may be revoked at any time before the action occe) Except for formal, individual evaluation and the initial provision of services to the student, consent may not be required as a condition of any other benefit to the parent or child. Any proposal or refusal to initiate or change the identification, evaluation, or educational placement or the provision of a free appropriate public education to the student after the initial placement is not subject to parental consent but is subject to prior notice as defined by subsection (1) of this rule.
    (f) Parental consent is not required before:

    1. Reviewing existing data as part of an evaluation; or,
    2. Administering a test or other evaluation that is administered to all students unless, before administration of that test or evaluation, consent is required of parents of all children. urs.
    (

    2

To Top

Start a New Topic » « Back to the eme5050 group