Audit+Report

** International School Aberdeen  ** ** October 2009  ** ** Final Report  ** For three days, October 5, 2009 – October 7, 2009, two Mathematics consultants, Janis Freckmann and Connie Laughlin, worked at the Aberdeen International School. Janis Freckmann examined the mathematics program in the Lower School and Connie Laughlin examined the mathematics program in the Upper School. They had three goals as part of their work at ISA:  1) Examine the alignment between the math curriculum and the math program with teaching and learning.   2) Examine the communication between staff at grade levels and across grade bands, transition between grade bands. 3) Examine the rigor and coherence of the mathematics program in preparation for the IB program.   They gathered data to address the above goals from various sources:   1) Teacher written survey done by all mathematics teachers prior to the onsite visit  2) Teacher classroom observations  3) Teacher individual upper school interviews 4) Grade Band (K-2, 3-5, 6-8, HS) and Administrator Interviews   This final report presents the findings from all the data that was gathered. The report is organized around the three goals. Below each goal, survey questions that address that goal are individually analyzed and discussed. Observations from the written comments about each question are summarized. This is followed by a brief summary of the information gleaned from the interviews and observations related to that question.    At the end of each goal’s questions and discussions, there is an overall conclusion formed from all information learned about the goal. There is also a section entitled ‘Next Steps’, which outlines suggestions for consideration that could be used for on-going improvements.    Finally, at the end of the report, there are 5 appendices:   A. Questions on the Teacher Survey  B. Responses from the Teacher Survey along with a complete listing of teacher comments  C. Interview questions used with Grade Level/Grade Band teachers  D. Interview questions used with the administrators  E. Observation Form used during classroom observations
 * Mathematics Curriculum Review **

  ** Goal 1  **:** Examine the alignment between the math curriculum and the mathematics program with teaching and learning ** **  Teacher Survey: Mathematics Program Question 1   ** ** I would rate the mathematics program (which includes the textbooks, additional teaching resources, assessments, and the school’s curriculum) as being consistent and coherent. **  // Teacher Surveys: // There is a clear discrepancy in the responses to this question from the lower school (83% agree) and the upper school (42% agree). This is not a surprise since the lower school is using the same textbook series for all grades K -5, and the upper school is using different textbooks in the middle school and in the high school. Also, the high school has begun serious discussions about consistency of using traditional American textbooks prior to the IB curriculum. // Interviews: //  · // Lower School: //Most teachers in Grades k – 5 implement the Bridges Mathematics textbook program as their core program. They feel the program has many components and it is difficult to pace through all of the program components. However, during the interview many comments were shared indicating a concern for students practicing their facts, and showing evidence of knowing their basic facts. Some teachers felt that the program did not have enough practice worksheets for students to become proficient with their basic facts. Both the lower school teachers and administrator feel the program offers hands on lessons that are coherent across grade levels. This enables teachers to address mathematical strengths and weaknesses of each student and move them along a continuum of learning//. //    · // Upper School: // In the Upper School, all the 6-8 grade teachers commented on the consistency and coherence of the program because they are all using the Prentice Hall Mathematics Series. They generally are very happy with this series. The 8th and 9th grade Algebra 1 classes use the same textbook, which again leads to consistency and coherence. Some of the High School teachers commented about the lack of a consistent approach to mathematics in the courses leading to the IB courses, since IB is an integrated curriculum and the courses prior to that are separate algebra and geometry courses. **  Teacher Survey: Mathematics Program Question 2   ** ** I am comfortable with the mathematics program I am teaching. **  // Teacher Surveys: // Overall the responses to this question indicate that almost all of the staff K – 12 has a sufficient background in mathematics to enable them to be comfortable implementing their math programs. It should be noted that some teachers are new to the grade they were teaching and were told to respond to this question based on their last year’s experiences. // Interviews: // · // Lower School: //The Lower School teachers indicated they were comfortable teaching this reformed based mathematics program. During the interview, some teachers expressed a concern about student worksheets. They felt the program did not offer enough paper and pencil drill activity sheets. · // Upper School: // In the Upper School teachers, all the high school teachers have strong mathematics backgrounds and are very comfortable teaching the courses that they are assigned to teach. One of the middle school teachers is primarily a science teacher, but has become comfortable teaching mathematics over the years. The other two middle school teachers reported that they like teaching math, and are confident in their ability to teach this subject. **  Teacher Survey: Mathematics Program Question 3   ** ** The mathematics program addresses the academic needs of all students. **  // Teacher Surveys: // This data from the teacher survey reveals that 50 % of the teachers agree that the math program meets the needs of all students and 50 % disagree with the statement. This is very interesting. Supplemental comments on the surveys indicate that teachers in both the upper and lower schools are concerned with differentiation and the lack of materials to meet the needs of all students** //. // **   // Interviews: // From the grade band interviews, teachers did not express any concerns about the ability to differentiate their lessons to meet the needs of all students.  · // Lower School: // Teachers felt that the math program offered plenty of resources for differentiation and teachers referred to the Bridges web site as an additional resource to support learning needs of all students. This topic may need further investigation and discussions between the administrators and the classroom teachers since the pre-survey data and the interview data are not aligned. The lower school administrator indicates a challenge for teachers is to meet the needs of all learners as students are coming to this school from various math programs with teachers using various pedagogical methods. During the classroom observations, some teachers in the Lower School were using modified assignments to address differentiation. Some teachers were also able to vary the type of questions they asked students during class or in small groups, depending on the students’ ability levels. // Upper School: // There was some concern about meeting the needs of all students in the Upper School. In the 6th and 7th grades, all students are heterogeneously grouped so teachers deal with academic differences by differentiating. In 8th grade, some students are in an algebra class and a small number are in a pre-algebra class, and the teachers feel that this meets the academic needs of the 8th grade students. In the High School, there is informal regrouping of 9tyh grade algebra students into 2 groups and then Geometry is also streamed into 2 groups. The three IB courses seem to meet the needs of the 11th and 12th grade students. Some of the Upper School teachers noted that they would like to see more horizontal enrichment in classes and not just vertical acceleration. **  Teacher Survey: Mathematics Program Question 4   ** ** I am confident that the mathematics I am teaching on a daily basis aligns to the school’s mathematics curriculum. **  // Teacher Surveys: // The different responses to this question at the upper school level compared to the responses at the lower school level reveals an interesting dynamic. The comments from the high school surveys indicate that they view that their own curriculum as aligned, but, because of observation of the skills of previous students and the lack of articulation between the schools, they were unsure that the upper school curriculum really aligns with the lower school curriculum. // Interviews: //  · // Lower School: //Teachers felt the program aligns to the school curriculum. However, they felt students need extra practice on skills such as regrouping with subtraction, using money to make change, and telling time. They felt there was strong alignment with mathematical ideas such as problem solving, writing story problems, and geometry with spatial reasoning. Teachers agreed with the spiral approach embedded in the program. <span style="margin: 0cm 0cm 10pt 18pt; mso-add-space: auto; mso-list: l31 level1 lfo3; text-indent: -18pt;"> · // Upper School: // The middle school teachers believe that the adopted textbook series aligns with the school’s curriculum. Once again, there was discussion during the high school teachers’ response to this question about the pre-IB curriculum. However, this year there have been conversations between the Algebra 2 teacher and the department chair to more closely link the necessary content emphasis between these two grades. <span style="line-height: normal; margin: 0cm 0cm 0pt 18pt; mso-layout-grid-align: none; text-indent: -18pt;"> **  Teacher Survey: Classroom Practice Question 1   ** ** My students have opportunities to solve complex problems, formulate and test mathematical ideas, and draw conclusions. **  // Teacher Surveys: // The teachers are reportedly confident that the mathematics program and their teaching practices allow students to engage in deep mathematical thinking. In the lower school only three teachers provided comments on this question and no consistent theme emerged and no detailed evidence was provided that this takes place in the classroom. In the upper school, there is consensus that the IB program does this well and less so in the other grades. // Interviews and Classroom Observations: // · // Lower School: //Although teachers agreed that their students engaged in deep mathematical thinking, formulated and tested mathematical ideas and drew conclusions, this big mathematical idea was not observed in classroom practice. Many teachers were using a guided approach to developing mathematical ideas and a guided approach for checking for student understanding. <span style="line-height: normal; margin: 0cm 0cm 0pt 36pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l31 level1 lfo3; text-indent: -18pt;"> · // Upper School:  // A hallmark of the IB curriculum and the Geometry curriculum is that students solve complex problems, formulate and test mathematical ideas, and draw conclusions. Therefore the high percentage of high school responses to this question is not a surprise. In the middle grades, the classroom observations did not observe this happening, but it could have occurred in other lessons during the week that were not observed. Since the Prentice Hall series is considered ‘traditional’, it is important that teachers do the parts of the lesson and homework that emphasize these ideas.
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   83%   ||   17%   ||
 * Upper School ||   42%   ||   58%   ||
 * ISA as a whole ||   63%   ||   37%   ||
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   84%   ||   16%   ||
 * Upper School ||   100%   ||   0%   ||
 * ISA as a whole ||   92%   ||   8%   ||
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   50%   ||   50%   ||
 * Upper School ||   50%   ||   50%   ||
 * ISA as a whole ||   50%   ||   50%   ||
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   100%   ||   0%   ||
 * Upper School ||   67%   ||   33%   ||
 * ISA as a whole ||   84%   ||   16%   ||
 * ||  Seldom/Monthly   ||   Weekly/Daily   ||
 * Lower School ||   18%   ||   82%   ||
 * Upper School ||   0%   ||   100%   ||
 * ISA as a whole ||   9%   ||   91%   ||

**  Teacher Survey: Classroom Practice Question 2   ** ** My students share their reasoning and justify their answers. **  // Teacher Surveys: // The math consultants found the responses from this question very interesting. Considering that this is a cornerstone of the NCTM Standards and is often cited as one of the best practices in mathematics, you would expect this to happen at least weekly if not daily. On the teacher survey, only about ½ of any grade band report that this is an important practice in their own classrooms. In the lower school four teachers reported using student reasoning during whole class discussions to develop the math lessons. In the upper school, teacher’s comments were mixed and did not indicate that this was a strong emphasis. // Interviews and Classroom Observations: // This data was confirmed in our brief classroom observations, which may not reflect the full scope of what is happening in the classrooms, since it was only a one-day observation in some classrooms. <span style="line-height: normal; margin: 0cm 0cm 0pt 36pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l23 level1 lfo7; text-indent: -18pt;"> · // Lower School: //In most classrooms, the learning goal was not posted. Because of this, it was not clear to the observer, and perhaps to the students, what mathematical ideas would be focused on and students would be learning during the lesson. Students need to be explaining their reasoning as they develop understanding of the mathematical idea of the lesson. Teacher’s questions should push for deep understanding of the mathematical idea so that as students explain their reasoning, teachers have an entry point to clarify concepts, refocus discussions and push for deeper understanding. <span style="margin: 0cm 0cm 10pt 36pt; mso-list: l2 level1 lfo11; text-align: justify; text-indent: -18pt;"> · // Upper School: // This data was confirmed in the interview and in brief classroom observations, which may not reflect the full scope of what is happening in the classrooms, since it was only a one-day observation in a particular classroom. In only one of the middle school observations was there a rich discussion and push for students to justify their answers. The other two teachers had less rich activities in which students explained their answers, but were not pushed hard to really justify their reasoning. Geometry and the IB curriculum in the high school naturally lend themselves to student reasoning and justification. **  Teacher Survey: Classroom Practice Question 3   ** <span style="line-height: normal; margin: 0cm 0cm 0pt 4.5pt; mso-layout-grid-align: none; tab-stops: -132.0pt;"> ** Classroom activities include the use of manipulatives and calculators to enhance students’ understanding of mathematics. ** <span style="line-height: normal; margin: 0cm 0cm 0pt 4.5pt; mso-layout-grid-align: none; tab-stops: -132.0pt;"> // Teacher Surveys: // Responses to this question varied by grade level. In the lower school, comments indicate the use of manipulatives more than the use of calculators. On the survey, comments from the upper school teachers always reported the use of calculators rather than manipulatives. In either case, this use is only about 50% of the time. // Interviews and Classroom Observations: // <span style="line-height: normal; margin: 0cm 0cm 0pt 18pt; mso-add-space: auto; mso-list: l31 level1 lfo3; text-indent: -18pt;"> · // Lower School: //Every classroom was well stocked with mathematics manipulatives. It was evident, in each classroom, that students are accustomed to working with math tools and are comfortable with using tools to represent their work. It was also apparent that students work well with their peers; partners or small table groupings. <span style="line-height: normal; margin: 0cm 0cm 10pt 18pt; mso-add-space: auto; mso-list: l31 level1 lfo3; text-indent: -18pt;"> · // Upper School: // The high school teachers routinely use calculators. The Geometry course makes extensive use of The Geometry Sketchpad so that students test conjectures and makes sense of the mathematics they are learning. The middle school teachers use calculators in problem solving situations and reported having two parts to some tests – one with calculators for problem solving and a second part without calculators that emphasize competence with numerical procedures. The use of other manipulatives was not widely reported nor observed. **  Teacher Survey: Classroom Practice Question 4   ** <span style="line-height: normal; margin: 0cm 0cm 0pt 4.5pt; mso-layout-grid-align: none; text-indent: -4.5pt;"> <span style="line-height: normal; margin: 0cm 0cm 0pt 4.5pt; mso-layout-grid-align: none; text-indent: -4.5pt;">** I use varied continuous assessments to evaluate both student progress and teacher effectiveness. ** <span style="line-height: normal; margin: 0cm 0cm 0pt 4.5pt; mso-layout-grid-align: none; text-indent: -4.5pt;"> // Teacher Surveys: // Again, there is an obvious difference in classroom assessment practices as reported on the Teacher Surveys. Referencing the research from Stiggins, it is critical that teachers have a balanced assessment system in place in their classrooms using both formative assessment data to guide classroom instruction and summative data for reporting purposes. The research clearly articulates that using both formative and summative assessment strategies will markedly improve student achievement. On the teacher survey, only 59% of the teachers used varied continuous assessments on a weekly or daily basis. The use of formative assessment strategies will inform teachers and students about student progress in learning. This question may have been misinterpreted and teachers may very well have a balanced assessment system in place in their classrooms. It would be important to collect more data from teachers on their classroom assessment systems both for guiding student learning and for reporting student progress. // Interviews and Classroom Observations: // · // Lower School: //However, data synthesized from grade band interviews indicate a different scenario from the data on the pre-survey. Teachers can fluently discuss the summative assessments they use to report student progress in achievement. These forms of assessments include student interviews, basic fact ongoing assessments, pre and post tests and chapter tests after a unit of study. These summative assessments were varied at grade levels and there did not appear to be a consistent plan of summative assessments. In discussions with teachers about their assessment systems, there does not appear to be a system of formative strategies to guide classroom practice. · // Upper School: // Upper School teachers uniformly report using formative assessment when they allow students to revise their homework, and possibly tests. This practice encourages students to reflect on what they had done wrong and correct those mistakes before any grading of the homework. However, there is not a consistent homework grading practice in the middle school or high school. <span style="background: #548dd4; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; display: block; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding-bottom: 1pt; padding-left: 4pt; padding-right: 4pt; padding-top: 1pt;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Goal 1: Examine the alignment between the math curriculum and the math program with teaching and learning. ** <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; line-height: normal; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Conclusion and Next Steps   ** // Conclusions: // Teachers in all grade levels reported satisfaction using the mathematics program and they are comfortable with understanding the mathematics they need to teach. After examining these eight questions that asked about the alignment between the math curriculum and the mathematics program with teaching and learning, teachers in the lower school feel strongly that Bridges textbooks are aligned across the grades. Middle school teachers in grade 6 and grade seven also feel the same way since they are using same book (Prentice Hall). The noticeable shortcoming here is the alignment between these two curricula and where they overlap. In our brief 3-day visit, we observed the same mathematical topic taught with the same rigor in both grades 5 and 7. Clearly some repetition is needed in these grades, but the middle school program should build on what has already been taught. In the high school the IB issue clouds the alignment issue. But even given this debate, there is general alignment of content across the high school courses. // Next Steps:  // · Read and discuss articles about best practices in mathematics, coming to consensus on practices that will be implemented across the grades · Develop common formative assessment strategies that can be used in all classrooms to support student learning (e.g., defining and sharing with students in kid friendly language the mathematics they will be learning) · Build teacher capacity for asking questions with a high level of cognitive demand · Analyze and learn from student work The purpose of these recommendations is to develop ownership in common best practices at ISA that would serve the needs of all students. First, teachers should deepen the understanding of formative assessment strategies, building on the work of Stiggens and Shirley Clarke. Secondly, teachers should focus on constructing good questions in a lesson that keep the mathematics at a high level of cognitive demand, building on the work of Peg Smith. This ensures that teacher instruction and student learning is always pushing toward deeper understanding. Lastly, we recommend an extension of the work already being done in grade level planning meetings. Teachers share student work in a structured activity, focusing on student misconceptions, successes and next steps that should be taken to further student learning. <span style="background: #548dd4; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; display: block; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding-bottom: 1pt; padding-left: 4pt; padding-right: 4pt; padding-top: 1pt;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0cm 0cm 10pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"> ** Goal 2: Examine the communication between staff at grade levels and across grade bands, and between the transition grade bands  **. **  Teacher Survey: Collaboration Question #1   ** ** I have opportunities for sharing ideas, resources, and best practices related to mathematics at my grade level. **  // Teacher Surveys //: From data gathered in the teacher surveys, communication within a grade level is excellent. In the upper school, considering that there is often only one teacher teaching any given grade level or subject, their responses are not a surprise. // Interviews: // The information that emerged from the interviews confirms the data presented in the chart above. This communication between grade level teachers is mostly informal, occurring during common planning times, lunch periods, in brief shared moments of ‘free time’. · // Lower School //: In the lower school, common grade level planning time may have a focus on mathematics. Teachers report they are using this time to plan lessons, construct lessons to co-teach, and plan interventions for student learning. · // Upper School //: In the upper school, since there is only one teacher for each subject it is not possible to hold conversations about teaching with anyone else. In teacher interviews, this was often noted as a negative side-effect of a small school. **  Teacher Survey: Collaboration Question#2   ** I have opportunities to meet across grade levels to discuss and collaborate on the mathematics program or address areas of concern. // Teacher Surveys: // Communication across grade levels or across grade bands is not as good as within grade levels, particularly in the Lower School. The Upper School is small enough that this communication was reported more frequently. // Interviews: // The information from the grade band meetings confirms these findings but also tells a slightly different story. · // Lower School: //In the lower school teachers would welcome the opportunity to meet more frequently with teachers across grade levels discussing topics such as the growing of mathematical concepts and skills, a common assessment plan, and challenges in meeting the needs of all students. The lower school administrator feels that the teachers need more professional development opportunities in mathematics. He would also like to support teachers as math leaders with on -site embedded professional learning in mathematics. · // Upper School: // In the upper school some communication occurs between the middle school teachers and the high school teachers, often in informal situations. However, they unfortunately reported that no collaboration occurs between the 5th and 6th grade teachers, leading to a situation where the grade 6 teachers really are unaware of what is happening in the grade below them. The middle school teachers would like more structured meetings with the high school teachers, like the recent whole 6-12 math meeting. <span style="background: #548dd4; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; display: block; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding-bottom: 1pt; padding-left: 4pt; padding-right: 4pt; padding-top: 1pt;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0cm 0cm 10pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Goal 2: Examine the communication between staff at grade levels and across grade bands, transition between grade bands   ** <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; line-height: normal; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Conclusion and Next Steps   ** // Conclusions: // Teachers in all grade levels reported satisfaction with the articulation within their grade or subject area. However, cross grade band articulation k - 5, and particularly at the grade 5 to grade 6 levels, should be improved. No evidence of focused conversations between these grade levels could be found. This is true to a lesser extent for the middle school mathematics teachers and high school mathematics teachers. There has been only one whole-department meeting of the math teachers in the last 2 years. // Next Steps:  // <span style="margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l32 level1 lfo18; text-indent: -18pt;"> · Cross grade level observations in classroom to observe the teaching and learning of mathematics between grades K – 5, 6- 8 <span style="margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l32 level1 lfo18; text-indent: -18pt;"> · Cross grade level observations and articulation between grades 5 and gr. 6 <span style="margin: 0cm 0cm 10pt 54pt; mso-add-space: auto; mso-list: l32 level1 lfo18; text-indent: -18pt;"> · High school observations to observe teaching and learning in courses above/below current teaching assignment The purpose of these observations is to develop coherence for student learning, to deepen understanding of how math ideas grow and to learn different instructional strategies. These observations should be followed by focused collegial conversation centering on student engagement, questions teachers ask to develop the mathematics, and reaching needs of all students. <span style="background: #548dd4; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; display: block; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding-bottom: 1pt; padding-left: 4pt; padding-right: 4pt; padding-top: 1pt;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0cm 0cm 10pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"> ** Goal 3: Examine the rigor and coherence of the mathematics program in preparation for the IB program  ** No specific question was asked on the teacher survey about IB Mathematics. The curriculum and final assessments for the IB Mathematics courses are externally set, so there is no way to change that. The Upper School is currently studying and discussing the coherence of the mathematics program prior to those courses in grades 8 through grades 10. In particular, the math teachers are debating whether to change the 10th grade book to an integrated approach that more closely matches the IB curriculum. It has been argued that an integrated approach to mathematics more closely aligns with the vision of mathematics as envisioned by National Science Foundation. Conversations with individual Upper School teachers and Franke Thomas revealed the following facts: · Achievement on the IB Tests has been consistently high for many years, and all during this time, the math department has been using separate books for Algebra 1, Geometry and Algebra 2. So, student achievement does not stand out as the main reason to change to a new approach to 10th grade mathematics. · The number of American students at ISA has declined to about 30%, so there is less need to have a curriculum that matches the American model: separate Algebra 1, Geometry and Algebra 2 courses. · The book currently used for the grade 10 Algebra 2 course is not a perfect match to prepare students for the IB Math program. Tim Gerry and Carrie Thomas have spent time this year identifying content areas in the Algebra 2 book that should be eliminated or de-emphasized as well as areas that should receive a more in-depth treatment. The department will need to assess these changes next year to see if students are better prepared for the IB program than before the changes were made. If these changes create a better content match between Algebra 2 and IB Math, then this will no longer be an issue. · A change of this importance requires that __all__ teachers in the department agree to it. Many well-intentioned changes in curriculum have failed over the years when even a small number of the staff does not agree with it and fail to fully support the new innovation. At this point, the math consultant was unable to determine the commitment of every member of the Upper School math staff to this proposed change to using integrated curriculum. · This decision involves the mathematics program from grade 8 through grade 10. Many questions will need to be asked and answered. Where does 8th grade algebra fit into this picture? Which courses will change? When should streaming begin? Will the 9th grade mathematics course change from a course on Geometry to an integrated approach? · Changing the grade 9 Geometry course to an integrated course will probably decrease the amount of geometry that students learn when they no longer spend a whole year on this content. · Rather than think about mathematics as ‘American Math’ vs. ‘European Math’, teachers should be encouraged to think about “Good Mathematics” to move this conversation forward. <span style="background: #548dd4; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; display: block; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding-bottom: 1pt; padding-left: 4pt; padding-right: 4pt; padding-top: 1pt;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; line-height: normal; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Goal 3: Examine the rigor and coherence of the mathematics program in preparation for the IB program   ** <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; line-height: normal; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"> <span style="background: #548dd4; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; line-height: normal; margin: 0cm 0cm 0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**  Conclusions and Next Steps   ** // Conclusions: //There are arguments for keeping the existing structure, just as there are arguments for changing to an integrated curriculum. After this short visit, the consultant has not been convinced that there is a compelling need for change. Ultimately, the decision should be made so that all the mathematics teachers support the curriculum that is used and that student achievement continues to be at a high level. // Next Steps // : Given the long-term importance of this decision, there needs to be on-going, in-depth discussions about this issue with all the Upper School mathematics teachers and the administration. These conversations need to lead to consensus about which curriculum to use.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none;"> || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  Seldom/Monthly   || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  Weekly/Daily   ||
 * <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none;"> Lower School || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  45%   || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  55%   ||
 * <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none;"> Upper School || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  33%   || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  67%   ||
 * <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none;"> ISA as a whole || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  41%   || <span style="line-height: normal; margin: 0cm 0cm 0pt; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 89.9pt; mso-element-top: 41.0pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; mso-layout-grid-align: none; text-align: center;">  59%   ||
 * ||  Seldom/Monthly   ||   Weekly/Daily   ||
 * Lower School ||   45%   ||   55%   ||
 * Upper School ||   33%   ||   67%   ||
 * ISA as a whole ||   41%   ||   59%   ||
 * ||  Seldom/Monthly   ||   Weekly/Daily   ||
 * Lower School ||   40%   ||   60%   ||
 * Upper School ||   33%   ||   67%   ||
 * ISA as a whole ||   41%   ||   59%   ||
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   100%   ||   0   ||
 * Upper school ||   50%   ||   50%   ||
 * ISA as a whole ||   82%   ||   18%   ||
 * || Strongly agree/ agree  ||  Disagree/strongly disagree  ||
 * Lower School ||   36%   ||   64%   ||
 * Upper School ||   83%   ||   17%   ||
 * ISA as a whole ||   53%   ||   47%   ||

**  Appendix A: Teacher Survey   ** **  August 2009   ** ** // Aberdeen International School  // ** ** // Teacher Survey   // ** ** // Name: Grade Level: // ** As you complete this survey highlight a numeric response and then briefly explain why you chose that rating. ** //  Mathematics Program   // ** ||  **  1  ** ** Strongly agree  **  ||  **  2  ** ** Agree  **  ||  **  3  ** ** Disagree  **  ||  **  4  ** ** Strongly disagree  **  || // Explain:  // ||      **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || //  Explain:  // ||      **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || //  Explain:  // ||      **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || //  Explain:   // || ** 1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  ||  **  Seldom  **  ||  **  2  ** ** Monthly  **  ||  **  3  ** ** Weekly  **  ||  **  4  ** ** Daily  **  || // Explain:  // || ** 1  **  ||       **  2  **  ||       **  3  **  ||       **  4  **  || //  Explain:  // ||      **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || //  Explain:  // || ** 1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || <span style="margin: 0cm 0cm 10pt 22.5pt; mso-layout-grid-align: none; tab-stops: 342.0pt 396.0pt 450.0pt 504.0pt; text-indent: -18pt;"> both student progress and teacher effectiveness. <span style="margin: 0cm 0cm 10pt 22.5pt; mso-layout-grid-align: none; tab-stops: 342.0pt 396.0pt 450.0pt 504.0pt; text-indent: -18pt;"> // Explain: // <span style="margin: 0cm 0cm 10pt 22.5pt; mso-layout-grid-align: none; tab-stops: 342.0pt 396.0pt 450.0pt 504.0pt; text-indent: -18pt;"> || ** 1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  ||  **  Strongly Agree  **  ||  **  2  ** ** Agree  **  ||  **  3  ** ** Disagree  **  ||  **  4  ** ** Strongly Disagree  **  || // What topics were discussed? //   ||       **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || //  What topics were discussed? //   ||       **  1  **  ||       **  2  **  ||       **  3  **       ||       **  4  **  || ** //   Future Planning    // ** What type of professional development would you recommend for math teachers in your grade band?
 * **  Answer the questions about the Mathematics program using a scale of 1 – 4 with 1 being strongly agree with the statement and 4 being strongly disagree.   ** ||
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-list: l27 level1 lfo35; tab-stops: -126.0pt; text-indent: -18pt;"> 1) I would rate the mathematics program (which includes the textbooks, additional teaching resources, assessments, and the school’s curriculum) as being consistent and coherent.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-list: l27 level1 lfo35; tab-stops: -126.0pt; text-indent: -18pt;"> 2) I am comfortable with the mathematics program I am teaching.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-list: l27 level1 lfo35; text-indent: -18pt;"> 3) The mathematics program addresses the academic needs of all students.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-list: l27 level1 lfo35; text-indent: -18pt;"> 4) I am confident that the mathematics I am teaching on a daily basis aligns to the school’s mathematics curriculum.
 * ** Answer the questions about // Classroom Practice and Collaboration // using a scale of 1 – 4 with 1 being seldom and 4 being daily.  **   ||
 * ** //  Classroom Practice and Collaboration   // ** ||  **  1  **
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l16 level1 lfo36; text-indent: -18pt;"> 1) My students have opportunities to solve complex problems, formulate and test mathematical ideas, and draw conclusions.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l16 level1 lfo36; text-indent: -18pt;"> 2) My students share their reasoning and justify their answers.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l16 level1 lfo36; tab-stops: -132.0pt; text-indent: -18pt;"> 3) Classroom activities include the use of manipulatives and calculators to enhance students’ understanding of mathematics.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 22.5pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l16 level1 lfo36; text-indent: -18pt;"> 4) I use varied continuous assessments to evaluate
 * ** // Collaboration  // **   ||  **  1  **
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 24pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo37; text-indent: -19.5pt;"> 1) I have opportunities for sharing ideas, resources, and best practices related to mathematics at my grade level.
 * <span style="line-height: normal; margin: 0cm 0cm 0pt 24pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo37; text-indent: -19.5pt;"> 2) I have opportunities to meet across grade levels to discuss and collaborate on the mathematics program or address areas of concern.