Table Of Content

Improve student A Mathematics conﬁdence and results and ScienceTrail with Australia’s premier online maths resource I n an attempt to engage primary-school students in a hands-on, real-world problem-solving context, a large urban KATHY HORAK SMITH district, a mathematics and science institute housed in a college of education, and a and SARAH QUEBEC corporate sponsor in the southwest United States, joined forces to create a mathematics FUENTES show how and science trail for fourth- and fifth-grade students. A mathematics and science trail mathematics and is a series of locations at which students answer mathematics and science questions, science may be connecting the environment to classroom > Cater for all ability levels with curriculum-based > Instantly create online or printable tests using the integrated via the use learning (English, Humble & Barnes, 2010; resources for Years 3-10. Cambridge HOTmaths Test Generator. Lewis & Lewis, 1998; Richardson, 2004; > Make maths meaningful with lessons, tutorials, > Save time in preparing activities and assessment tasks, of a mathematics/ Rosenthal & Ampadu, 1999; Shoaf, Pollak questions and walkthroughs. marking and recording. & Schneider, 2004; Simmons & Byrne, 2007; > Ignite student interest with interactive investigations > Easily assign tasks in the classroom or at home with the Spangler, 2004; The National Math Trail, science trail. and animations. Task Manager tool. 2006). The environment is limitless because > Challenge your students with assessment questions > Track class and student progress with diagnostic a trail can take place in a school (e.g, at four levels of difﬁculty. assessment tasks and reports. Richardson, 2004), on school grounds (e.g., Spangler, 2004), or within or beyond a community (e.g., English, Humble & (e.g., Australian Curriculum, Assessment Barnes, 2010; Rosenthal & Ampadu, 1999). and Reporting Authority [ACARA], 2011; Now integrated with Cambridge texts for an Even though suggestions have been made National Council of Teachers of Mathematics exceptional text and online package. to incorporate multiple subjects on trails [NCTM], 2000; Victorian Curriculum (Richardson, 2004; Spangler, 2004), the Assessment Authority [VCAA], 2009). For majority of the literature describes trails instance, the new Australian Curriculum: based on one area, such as mathematics or Mathematics acknowledges the application science. of mathematical skills within the science Put us to the test! The trail described in this article curriculum: includes both mathematics and science. Practical work and problem solving Educational organisations the world over across all the sciences require the Trial Cambridge HOTmaths with your class for one term encourage teachers to make connections capacity to organise and represent data between mathematics and other disciplines in a range of forms; plot, interpret and www.cambridge.edu.au/hotmaths/termtrial www.cambridge.edu.au/hotmaths • Cambridge HOTmaths TM ABN 13 094 237 233 • 477 Williamstown Road, Port Melbourne VIC 3207 APMC 17 (2) 2012 19 Smith and Fuentes extrapolate graphs; estimate and solve become an annual event. In addition, each ratio problems; use formulas flexibly year the primary school pre-service teachers in a range of situations; perform unit are involved in the execution of the trail. conversions; and use and interpret rates For example, the pre-service teachers have including concentrations, sampling, written and revised questions for the trail. scientific notation, and significant Figures 1 and 2 include some of the figures (ACARA, 2011, Organisation mathematics and science questions for two section, para. 4). of the sites. At the clock tower location Bosse, Lee, Swinson, and Faulconer (2010) (Figure 1), there is a bike rack for which found a close alignment in the way students the students need to estimate the length of learn mathematics and science. The findings the curved metal pipe and then measure of this research support the inclusion of the actual length, comparing it to their mathematics and science on our trail. estimates. A primary school student wrote The remainder of the article describes the about her experience answering this question development and implementation of this in a thank-you note: “I liked [the] bike rail ongoing project, the benefits of participation and measure[ing] it and I was surprised it in a trail, and advice for those considering was 20 ft.” The student’s comment reflects developing a trail. a misconception that some children have regarding the length of compact and crooked paths (Van de Walle & Lovin, 2006). Laying the groundwork for the trail At this locale there are also netbooks and ProScopes© (handheld microscopes that To foster collaboration between the university transmit pictures of objects to a computer and local school district, the Mathematics screen) with which students explored the and Science Institute agreed to host an contents of the soil. At a fountain (Figure activity day on campus for primary school 2), students used science equipment to test students. As a mathematics education water quality and had to use problem-solving professor housed in the institute and based strategies to measure the fountain’s diameter on my previous experience in writing and circumference, as well as explore the and implementing mathematics trails for relationship between the two quantities. pre-service and in-service teachers, I suggested Twenty schools participated on each day inviting primary schools to participate in a that the trail occurred. Every school sent mathematics and science trail, which has a team comprised of one teacher and six There is a bike rack on the Go to the fountain. Look at the water south side of the clock tower. carefully and describe how it smells Predict the length of the pipe if and looks. There are several tests you stretched it out so that the that can tell us more about water. pipe was straight. How did you Test for the following: pH, GH and make your prediction? Use the nitrite levels. What does this tell you tape measure to measure the about the water in the fountain? pipe. How do your prediction and What is the temperature of the water measurement compare? in degrees Fahrenheit and degrees Celsius? What would happen if the temperature of the air was 30 degrees Fahrenheit? Use the ProScope© to look at a Find the diameter of the fountain in feet. Explain how you measured the sample of soil from the grassy diameter. What is the length around (circumference of) the fountain in lawn. Describe what you see in feet? Based on your diameter, what is the radius of frog fountain? Show the soil. your calculation. What is the relationship between the diameter and the circumference? Figure 1. Two of the revised questions for the clock Figure 2. Questions for the fountain station. tower station. 20 APMC 17 (2) 2012 A Mathematics and Science Trail The windowpanes of one side of science trail at their schools. the Ballet Building are rectangular On the day of the trail, the pre-service prisms. Look at the face of each teachers are assigned one of two roles: site rectangular prism. How many single windows are there? facilitator or team guide. Two site facilitators How many double windows are there? remain at each location while each primary How many triple windows are there? school is led through the site rotation by Find a pattern in determining the total the team guide. Each site facilitator receives number of rectangles. (Hint: There are more than individual rectangles.) a box of materials necessary to complete the mathematics and science questions at Look at the rocks along the sidewalk. their particular locale. Team guides greet What is growing on the rocks? Explain how it grows on the rocks . their assigned schools providing them with t-shirts and a backpack of supplies, including Figure 3. Example questions from the trail for the a binder with the questions, job assignment classroom teachers. tags (supply carrier, task master, measurer, students (three fourth-graders and three recorder and leader), and pencils. Starting fifth-graders; three males and three females). at different locations, pairs of teams spend In particular, schools are encouraged to select twenty-five minutes at each site with ten children who are not typically recognised for minutes allotted for travel between stations. their academic achievements. By choosing After three hours on the trail, the students these students to participate in this special congregate for a lunch of, in the words of event, the intent is to develop their confidence one of the primary school students, “college in the academic arena. pizza.” As the students depart, they receive a Prior to the day of the trail, the primary certificate of participation. school teachers attend a workshop. The purpose of the professional development is fourfold. First, the teachers are exposed The multifaceted outcomes of the trail to the idea of a mathematics and science trail by reading articles related to the topic Some of the teachers have heeded the (Richardson, 2004; Spangler, 2004). The suggestion about creating a trail at their participants experience a trail, different schools. For example, one of the primary from the one created for the primary schools generated a trail with a parallel set school students, which includes content of developmentally appropriate questions that challenges them as learners. (Refer to for each grade level at each station (Figure Figure 3 for examples: a counting question, 4). Even though the original intent was that which involves noting patterns, and a biology the teachers would go back and write the question, which requires the identification questions themselves, they have incorporated of plants.) Once the trail is completed, the teachers return to the classroom to discuss Kindergarten, First, and Second their observations and the expectations for the Go to the two trees in the front lawn. Start at one tree and count how upcoming trail for the students. In particular, many footsteps it takes to get to the other tree. the pre-service teachers are responsible for Third and Fourth Go to the two trees in the yard with the sign. Using the tape measure, engaging and assisting the primary school measure the distance between the two trees in yards. students in answering the questions at each Fifth site. The primary school teachers are asked to Go to the two trees in the yard with the sign. Using the tape measure, serve in a supporting role as the pre-service measure the distance between the two trees in yards. Now convert the teachers gain practical experience working distance into feet. Finally put it into inches. with children. Lastly, the classroom teachers Figure 4. An example of a parallel set of grade-appropriate are encouraged to design a mathematics and questions at a station at a primary school. APMC 17 (2) 2012 21 Smith and Fuentes able to incorporate the writing process with mathematics and science content. Similarly, students at a different school created a mathematics trail for a lower grade level. One of the questions required students to measure the length of fence using the ancient measurement of a cubit (length Figure 5. An example of student-generated questions prior to being revised. of one’s forearm), as depicted in Figure 6. The students then compared measurements, the production of the trail into their lessons, discovering the need for standard units. In thus enabling the students to be the authors implementing the trail, the students became and editors of the questions. One teacher facilitators for their younger peers, providing had the students brainstorm ideas (Figure 5). opportunities to communicate about the After he consolidated this information, as a mathematics. class, they revisited and revised the questions. Another teacher shared the following information about the process used at her Benefits of the trail particular school: As a team we went around and took Pre-service teachers, classroom teachers, pictures of the school. Then we went university faculty, school district back and presented example questions administration and a corporate sponsor and explained that as a 5th grade came together to provide a hands-on project we would be using the photos mathematics and science trail for the benefit and personal observations to continue of primary school students. In their letters, to write and develop questions for not the students’ words bespoke the impact of only 5th grade but all the grade levels in participating in the trail. Even though many the school. … The students even went of the students wrote how they had fun on the so far to asking me to help them make trail, several students’ comments specifically sure they were grade level appropriate addressed different aspects of their learning and involved the [state standards]. I of mathematics and science: “I think it is helped with editing the initial questions important to remember that math and science and after that the classes took control is part of your life. You use them everyday.” and took off. … They didn't see this as This student was able to see that mathematics a math or science or writing project. It and science are not just school subjects, but was a challenge that was fun for them she saw their value as they applied to her because they were doing it for the rest world. “I learnd [sic] that you alwas [sic] have of the school. to make good obsertations [sic] and have As indicated in these comments, by good back up details to support them.” In directly involving students, the teachers were addition to the academic content of the trail, this student also developed an understanding of a basic process in problem solving. This collaboration not only benefitted the primary school students but also enabled the practicing teachers to develop professionally. The classroom teachers were able to observe the primary school students’ enthusiasm. Unlike many professional development offerings, the teachers saw what they had read Figure 6. A student measuring the length of a fence in cubits. 22 APMC 17 (2) 2012 A Mathematics and Science Trail about and had an experience as a learner in Authors’ note action with the primary school students on the day of the trail. Despite participating in two The mathematics and science trail was different trails, the teachers cannot duplicate partially funded by Chesapeake Energy either campus trail at their school. They will and the Andrews Institute of Mathematics need to create a trail based on the physical and Science Education in the College of aspects of their school site that will meet the Education at Texas Christian University. unique needs of their colleagues and students. By coordinating the professional development in concert with the student trail, several of the References classroom teachers were encouraged to take Australian Curriculum, Assessment and Reporting the initiative to involve their school community Authority [ACARA]. (2011). Australian curriculum: in an ongoing effort of building a site-based Mathematics. Retrieved from http://www. australiancurriculum.edu.au/Mathematics/ trail. With plans to have these innovators share Rationale their successes and challenges in the future Bosse, M. J., Lee, T. D., Swinson, M. & Faulconer, J. (2010). The NCTM process standards and the five professional development sessions, they not Es of science: Connecting math and science. School only are teacher-leaders within their school Science and Mathematics, 110(5), 262–276. but also the district. English, L. D., Humble, S. & Barnes, V. E. (2010). Trailblazers. Teaching Children Mathematics, 16(7), 402–412. Lewis, T. R. & Lewis, C. H. (1998). Take it outside! Insights and recommendations for Teaching Children Mathematics, 4(8), 462–463. planning a trail National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author. For readers who are considering creating Richardson, K. M. (2004). Designing math trails for the elementary school. Teaching Children Mathematics, a trail, whether implemented on a large 11(1), 8–14. scale with multiple schools or a smaller Rosenthal, M. M. & Ampadu, C. K. (1999). Making mathematics real: The Boston math trail. Mathematics scale for one school, here is some advice Teaching in the Middle School, 5(3), 140–147. based on the experiences discussed in this Shoaf, M. M., Pollak, H. & Schneider, J. (2004). Math article. Significant time is required for trails. Lexington, MA: COMAP. Simmons, C. & Byrne, J. (2007). Gearing up for planning a trail. First, brainstorm potential mathematics. Mathematics Teaching in the Middle collaborators in your community who have School, 13(4), 220–223. a vested interest in promoting innovative Spangler, L. (2004). P.H.Y.S.I.C.S. can be done! Science and children, 41(6), 30–33. educational endeavours. Next, establish The National Math Trail. (2006). Retrieved from http:// academic goals by identifying content and www.nationalmathtrail.org learning processes that enhance the current Van de Walle, J. A. & Lovin, L. H. (2006). Teaching student-centered mathematics: Grades 3–5. Boston: curriculum. Subsequently, select sites with Pearson Education. unique features that promote your objectives. Victorian Curriculum and Assessment Authority [VCAA]. (2009). Victorian essential learning standards. Retrieved Once goals and locations are determined, from http://vels.vcaa.vic.edu.au/maths write, edit, field test, and revise questions. In addition to the example questions provided in this article, refer to the reference list which is a rich resource for building a trail. Kathy Horak Smith An option is to include students in this Tarleton State University, USA process, as it involves the integration of <[email protected]> writing with other content areas. Lastly, a Sarah Quebec Fuentes trail is a living document; it is always evolving Texas Christian University, USA reflecting physical, curricular, and human <[email protected]> resource changes. Happy trails. APMC APMC 17 (2) 2012 23