You could never find this in a M easurement is a mathematics skill MARY BARR GORAL students encounter often in their daily lives (Reys, Lindquist, and Lambdin, Smith, and Suydam, 2004). The act of measuring involves the use of concrete, PATTY GILDERBLOOM hands-on materials that students find engaging and appealing. According to provide an insight into Martinie (2004), the best way to teach meas- urement “is to find or create situations in a Grade 5 classroom which students need to measure and let them experience this process” (p. 431). Preston where students were and Thompson (2004) concur that “the most fundamental aspect of measurement is the act involved in a of measuring” (p. 438). The measurement lesson we presented to a group of grade 5 real-world project students is a good example of how measure- ment can provide a hands-on experience that which enhanced their is off the traditional “beaten path” of the typical daily maths lesson and enlist the measurement skills. students in enjoyable, real world work. Solving a problem From the beginning of the school year, Patty’s grade 5 students argued regularly over the baskets of coloured pencils used for art activ- ities. The pencils were loose and in no particular order, which made it difficult for children to find the colours they wanted. Some pencils were quite small, and these were the least desirable for the children. This problemtookawayvaluableinstructionaltime. APMC13(1)2008 BarrGoral&Gilderbloom SowhenMary,aprofessoratalocaluniversity, to assess students’ understanding of linear suggestedhelpingthestudentswithameasure- measurement. Furthermore, it was an oppor- ment project involving the creation of pencil tunity to engage students in an investigative cases through sewing, Patty saw this as a and problem solving aesthetic experience. In valuableteachingopportunity.Thepencilcases addition, the pencil case project would satisfy would make it possible for each student to what Reys et al. (2004, pp. 391–392) believed have their own set of pencils. Not only would were reasons for including measurement in Patty’sGrade5studentshaveachancetosolve the mathematics curriculum: an ongoing problem, they would also have • It provides many applications to an opportunity to practice their linear measure- everyday life. ment skills in a hands-on, practical manner. • It can be used to help learn other math- ematics. • It can be related to other areas of the Teaching measurement school curriculum. • It involves students in active learning. Although very little research, if any, exists on • It can be approached through problem the use of sewing projects to teach measure- solving. ment, some studies have shown connection between intellectual development and handi- work, such as knitting and sewing. According The project to Schwartz (1999), “Recent neurological research tends to confirm that mobility and Although students did not require previous dexterity in the fine motor muscles, especially sewing experience, they were taught how to in the hand, may stimulate cellular develop- thread a needle, tie a knot, and sew two basic ment in the brain and so strengthen the stitches — the running stitch and the blanket physical foundation of thinking” (p. 248). We stitch. Costs associated with the project were have found that ongoing integration of hands- minimal, and largely dependent on the type onworkintothemathematicscurriculumtends of fabric used. The materials required for a to sustain children’s attention and interests. class of 25 students were as follows: Even though Patty’s grade 5 students • 60 pieces of sturdy fabric (e.g., felt or knew the basics of linear measurement, it denim) of various colours, measuring was believed that the project could be used 31.5 × 23 cm; Figure1 Figure2 24 APMC13(1)2008 Youcouldneverfindthisinashop! • 250 pins; made per centimetre. NCTM’s (2000) • 25–30 embroidery needles; Measurement Standard expectations for • 30 packages of sewing thread, various students in grades 3–5 recommends that colours; students learn to select and use benchmarks • 7.5–9 metres of thin ribbon; to estimate measurements. Using mathemat- • 25 rulers; ical language in context helps children • 25 pieces of tailor’s chalk; remember and sustain the terminology. The • 25 pairs of scissors. next step involved sewing the individual slots As shown in Figure 1 the measurements for the pencils, using the simple running for the three pieces of felt needed for the stitch. However, before this stitching began, cases were: additional measuring was required. The slots 1. 31.5 cm × 23 cm for the pencils measured 2.5 cm. In order for 2. 31.5 cm × 9 cm the stitches to be straight, it was important to 3. 31.5 cm × 6 cm measurethe2.5cmincrementsonthebottom Measuring the first piece proved more as well as on the top of this piece of material, challenging than originally expected. Some then connect the marks with a chalk line (see students did not know where to lay their ruler Figure 3). Most students successfully to begin measuring and needed assistance. completed this measurement activity, Others did not know how to measure 0.5 cm. although a few children experienced diffi- Fortunately, the students who initially strug- culty with holding the ruler and connecting gled when measuring the first piece needed the marks. little or no help by the time they measured Once the 2.5 cm slots were measured, and cut the second and third pieces. marked, and connected, students could begin After everyone had measured, marked with sewing. There was one tricky part to this chalk, and cut their material, the next step portion of the project. After stitching the first was to pin everything together (see Figure 2). line with the running stitch, the stitch going When the pinning was successfully across to the second line was to be only on completed, and students rounded the corners the top portion of the fabric. In other words, with their scissors, they were ready to begin it could not go through both pieces because sewing. Students were instructed to stitch all the pencil would not be able to be inserted. around the perimeter of the pencil case and This made perfect sense to the students, and asked to estimate the number of stitches no one made that mistake. Figure3 Figure4 APMC13(1)2008 25 BarrGoral&Gilderbloom Two more measurement activities were not know how to find half a centimetre. Two required in order to finish the pencil cases. students used problem solving when they Students first needed to measure and cut a 3 realised their piece of material was 30 cm cm square of material. They then had to wide rather than 31.5 cm. “When I found out measure and cut a 61 cm piece of ribbon. my piece of material wasn’t exact, I thought The 3 cm square piece of material and the all my other measurements would be off, but ribbon were necessary to close the pencil I trimmed them to the size of my original case. The square of material was sewn on the piece and it worked out.” back middle portion of the case on three Students also provided interesting insights sides with the blanket stitch. Before finishing regarding other things they learned as a result the fourth side, the ribbon was doubled, of the project. One student commented that inserted and sewn in (see Figure 4). she was able to work with measuring the perimeter and that was a good hands-on experience for her. The following students’ Insights from the children comments reinforced our hope that this project encouraged mathematical thinking: The students were pleased with their finished • “You have to think about it in mathe- products and faces lit up with smiles of matical terms or else you may mess up accomplishment and satisfaction. We decided a whole bunch.” to ask students questions about the project in • “Some people’s minds can’t think with order to gain insight as to how something numbers; they have to show what they like this helped them with measurement. know in a practical way.” Students’ answers ranged from feeling Many comments from students actually fell quite confident in their ability to measure to into the realm of the affective learning envi- admissions regarding their lack of experience ronment. According to The Australian with rulers. A few students commented that Association of Mathematics Teachers’ measuring was hard because they had not Standards for Excellence in Teaching had a lot of experience with it and there was Mathematics in Australian Schools (2006, confusion using the ruler. Another child said Domain 3), it is critical for teachers to address that measuring was difficult because he did the psychological, emotional, and physical needs of students. Many students shared with us that they found out maths could be fun. One student mentioned that the pencil cases were a practical project as well as a learning experience. Another student mentioned that projects are fun and you end up with a “story and a product.” Given that one of the benefits ofteachingmeasurementisitspracticalnature, we were pleased with the fact that many students realised the connection between mathematics and practical types of projects. Finally, students shared with us some personal thoughts. One child commented that this project allowed her to put heart and emotion into it, whereas if she bought a pencil case from a shop, it would not feel the same. Schwartz (1999) concurs: “In an age Figure5 when children are too often encouraged to 26 APMC13(1)2008 Youcouldneverfindthisinashop! become passive consumers … engaging in … instruction, because students could work at hand[i]work can be a powerful way of their own pace and receive help when bringing meaning into a child’s life” (p. 256). needed from the adults or from other Students also told us that it felt really good to students who worked more quickly. The finish a project and to accomplish something initial problem of arguing over coloured that was challenging. Others loved the quiet pencils was solved, as the children each now and relaxing nature of the project. In winding had their own complete set of pencils. up our discussion, one student shared that According to Wilson and Osborne (1988, in her pencil case was something she would Reys et al., 2004), “Because most research “treasure and use forever.” does not clearly stipulate just how teachers should plan for instructional lessons on the subject of measurement, students should be Reflections given frequent opportunities to use measure- ment in their school experience, most After the pencil case activity was over, we preferably through real-life work projects that reflected on both the positive and negative involve doing and experimenting rather than aspects of the lesson. As teachers, we were by passively observing” (p. 109). When both surprised about how confusing meas- elementary age children are presented with uring could be, even for grade 5 students. We measurement activities as something they can cameupwithafewsuggestionsforimproving engage in rather than simply watch, the expe- the process we used with the students: rience for them provides involvement and • Have all the steps to the meas- enjoyment, along with the practice of standard uring/sewing project written down on a measuring skills necessary in everyday life. large sheet of paper (preferably with illus- trations). Include step by step instructions and highlight all measurements. References • Review where to begin measuring with Australian Association of Mathematics Teachers. the ruler, and how to read all the ruler’s (2006). StandardsforExcellenceinTeaching lines. MathematicsinAustralianSchools. Adelaide: AAMT. • Review horizontal and vertical, using Martinie, S. (2004). Measurement: What’s the big idea? descriptions such as “like the horizon” and MathematicsTeachingintheMiddleSchool,9, “up and down”. 430–431. National Council of Teachers of Mathematics. (2000). • For the sewing part of the lesson, review CurriculumandEvaluationStandardsforSchool threading a needle, how much thread to Mathematics. Reston, VA: NCTM. Preston, R. & Thompson, T. (2004). Integrating meas- use, single or double threading, and urement across the curriculum. Mathematics model/go over all the required stitches. TeachingintheMiddleSchool,9, 436–441. • Group the students more effectively in Reys, R., Lindquist M. M., Lambdin, D. V., Smith, N. L. & Suydam, M. N. (2004). HelpingChildrenLearn teams. Integrate strong/weak children in Mathematics,(7thed.). Hoboken, NJ: John Wiley both math and sewing skills. Intersperse and Sons. good listeners with ones who need more Schwartz, E. (1999). MillennialChild. Hudson, NY: Anthroposophic Press. help focusing, and combine fast and slow workers, so the speedier finishers could be available to help those struggling and straggling. Mary Barr Goral, Bellarmine University, KY, USA Making the pencil cases appeared to be a <[email protected]> successful project for Patty’s class. All Patty Gilderbloom, Byck Elementary, KY, USA students were involved and the lessons them- APMC selves were a model for differentiating APMC13(1)2008 27