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Vol X No. 2 Summer |
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 Photo credit - Rebecca Gammill Bowl by Baltic by Design
It has been a very busy but exciting school year! There have been so many times when I said to myself, "Well, that will have to wait until summer." As I look at my To-Do list, I think that I need for my summer break to last as long as a school year just to get started on all of these tasks. (I may have a procrastination problem.) I have so many contacts to make, books to read, topics to research, new ideas to ponder, and activities to create. I thought that as I accumulated more years of teaching experience that eventually my need to learn new things would slow down. The opposite appears to be true. The more experience I gain, the more I want to learn and think deeply about ideas. I am also realizing that many of my previous understandings are full of misconceived notions. After attending the 2018 NCTM Annual Conference this year, I added one more book to my summer reading list - Catalyzing Change in High School Mathematics: Initiating Critical Conversations. With his President's Address, Dr. Matt Larson launched the release of this research-based resource that identifies and addresses critical challenges in high school mathematics to ensure that each and every student has the mathematical experiences necessary for his or her future personal and professional success. I was also impressed to discover the 2018 NCTM Annual Conference included a heavy representation of Georgia educators in various capacities. We had a GCTM member on the 2018 NCTM Program Committee, more than 25 presenters, 3 representatives at the Delegate Assembly, and countless participants in Washington, D.C., for this tremendous event. It was great to see so many familiar faces and hear those Southern accents in the sessions that I attended. Their participation reflected the dedication of Georgia educators to help our schools and students continue to grow and improve. GCTM is excited to showcase several of the nationally-recognized speakers from the NCTM Annual Conference at the 2018 Georgia Mathematics Conference. Dr. Thomasenia Lott Adams, 2018 NCTM Program Committee Chair from the University of Florida, will be kicking off the Georgia Math Conference on Wednesday night. Dr. Matt Larson, NCTM Immediate Past President, will be the keynote for Thursday night. Dr. James Tanton, an ambassador for the Mathematical Association of America and a purveyor of joy in mathematics, will be the Closing Keynote on Friday afternoon. While attending the NCTM annual conference, I also had the privilege of meeting and attending a session led by one of our featured speakers, Dr. Kristopher Childs, from Texas Tech University. Needless to say, with this many bright minds converging again at GMC, I highly recommend that you make your plans to attend. Try to arrive early as we have special plans for Wednesday afternoon, and stick around Friday afternoon to hear Dr. Tanton. For more details about GMC, visit www.gctm.org .GCTM is also providing opportunities for professional growth over the summer. Don't forget to register for the 2018 GCTM Summer Academies that take place in June and July. Now is a great time to watch the grade-level videos "What Do Mathematics Standards Look Like in the Classroom?" released by the Georgia Department of Education. Look for more of these videos to be released this summer. With all these activities going on this year, it will be important to find some time to relax, refresh, and spend meaningful time with family and friends! I hope everyone has a great summer, and I hope to see you all at some of these events. If you have any questions about what GCTM has to offer, please contact your GCTM Regional Representative or any member of the Executive Committee . We wish to better serve you and your interests as a mathematics teacher.
2018 Legislative Session Report In the early hours of the morning
on March 30th, 2018 the Georgia General Assembly completed its
40-day legislative session and adjourned "Sine Die." After
adjournment, the Governor has 40 days to sign or veto bills. If the
Governor does not sign or veto a bill, it will automatically become
law. The Governor has the power of line-item veto over the budget
bills. Throughout the legislative session, the advocacy team
identified and analyzed legislation of interest to GCTM and worked
with the appropriate decision-makers to determine what action (if
any) should be taken. K-12:
HB 787: Rep. Scott Hilton (R-Peachtree Corners) filed this piece
of legislation that seeks to bridge the gap between existing funding
sources for local charter schools/public schools and state charter
schools. Currently, state charter schools receive money from the
state along with a small supplement equivalent to the average
per-student local funding of the five poorest school systems in the
state. HB 787 would increase the supplement: 1) to the state average
per-student funding level for schools with statewide attendance
zones and 2) for those with smaller attendance zones to the greater
of local district revenue or the average of the state's five poorest
systems. After this bill cleared the House a number of significant
changes were made in the Senate Education Committee at the request
of public education advocates although they were later reversed on
the Senate floor at the urging of Lt. Governor Cagle who is a strong
charter school advocate. After some additional changes were made on
the House floor, the Senate agreed to the changes and the bill was
transmitted to the Governor for his signature or veto. Higher Education:
The GCTM Middle School Math Tournament was held
at Tattnall Square Academy on April 21, 2018. Middle schools across
the state were invited to register up to eight students to compete.
The tournament consisted of a 30 question multiple-choice test with
a 45-minute time limit; 10 individual ciphering problems, each
problem with a two-minute time limit; 3 rounds of four pair
ciphering problems (in which students from a school formed teams of
two), each round with a four-minute time limit; and a four-person
team "power question," in which the team solves a complex problem
with a 10-minute time limit.
Sixty-one students from twelve schools participated. Sponsors that are members of GCTM only had to pay a $10 registration fee or submit five multiple-choice questions for possible inclusion in a future tournament. The next GCTM middle school tournament is scheduled for April 20, 2019.
The 42nd annual GCTM State Math Tournament was held at Middle Georgia State University in Macon, Georgia on April 28, 2018. Schools are invited to the state tournament based on their performance on previous Georgia tournaments throughout the 2017-2018 school year. Thirty-six invited schools attended this year's state tournament. Four students are selected by their school sponsor to represent each school (one school brought a team of two). Twenty individuals were also invited to try-out for the state-wide Georgia ARML team, making a total of 162 participants.
The tournament consisted of a very challenging
written test of 45 multiple-choice questions and 5 free-response
questions with a 90-minute time limit; 10 individual ciphering
problems, each problem with a two-minute time limit; and a team
round. The team round consisted of 12 problems for each team to
solve while working together within eighteen minutes.
Fulton Science Academy
An item analysis of the competition problems was completed at the state tournament. The responses analyzed included the 45 multiple-choice problems on the written test and the 10 problems from the individual ciphering round. Before we discuss what the item analysis revealed, some background information would be useful. The problems on the written test are designed to increase in difficulty. Thus, theoretically, problem 1 is the easiest multiple-choice problem and problem 45 the most difficult multiple-choice problem on the test. Below are those problems.
Test Problem #1: What is 15% of 0.75 of 48/30?
Problem 44 seems like a geometry problem, but it is, in fact, a trigonometry problem, which turns into a calculus problem! For angle GFH to be acute, the sum of the other two angles along the side of the square (angles BFG and CFH) must be greater than 90 degrees. Since these other two angles are in right triangles, we can express these angles as inverse tangents of the portions of the side of the square opposite the angles; call these portions x and y. From the inequality arctan(x) + arctan(y) > p/2 then leads to the inequality y > cot(arctan(x)). But since the cotangent of the inverse tangent of x is 1/x, we see that y > 1/x. Hence, we want the area of the square which lies above the hyperbola y = 1/x, and this is calculated using a definite integral. The probability is the area above the hyperbola which lies in the square over the area of the square. This is (3--ln(4))/4.
Problem 45 can be solved by noticing that the entries in the array are the finite differences of the Fibonacci sequence; that is, an entry in the array is the difference of the two terms above it. Adding all the combinations of all the leading differences yields D0,6 which is the sixth Fibonacci number: 8.
For the most difficult ciphering problem, there was a tie! Only 12 participants gave the correct answer to the following two problems.
Once again, it is a conic section problem that is
considered a difficult question. This is normal over the last few
years; apparently the teaching and learning of conic sections is no
longer a priority. The answer to this problem is 12.
Ciphering Problem #5: A function from a set X
to a set Y is said to be onto, or surjective, if for all y
in Y, there exists an x in X such that y =
f(x). Compute the number of onto functions from the set {1, 2,
3, 4, 5} to the set {A, B, C, D}.
Two elements in X must be mapped to the
same element in Y; there two elements in X can be
chosen in 10 ways. These two elements can be mapped to any of the 4
elements in Y, and this leaves 3! = 6 ways to map the
remaining elements. The answer is 10 ' 4 ' 6 = 240.
Have you ever wondered whether what you ate caused you to have food poisoning? The CDC uses two-way tables to determine a contaminant of foodborne outbreaks. At NCTM in Washington, D.C., Michelle Mikes and I lead an engaging STEM simulation for teachers to help students understand the purpose and use of two-way tables. We adapted our presentation from a STEM conference session that we attended led Dr. Ralph Cordell. This lesson was designed for 8th-grade students to learn how ratios, two-way tables, and probability can be used to determine details about food poisoning contaminants. But, you can take this lesson and adapt it for use in elementary or high school classrooms.
Participants first learn some background information on food poisoning: what defines an outbreak, symptoms and causes of food poisoning, the highest causes of foodborne illnesses and deaths, the early thoughts about diseases, types of foodborne germs, and information from articles and radio posts. For example, did you know that food should not sit out at room temperature for more than 2 hours or that you shouldn't eat any leftovers that are more than 4 days old? This information was provided by Dr. Sanjay Gupta, Chief Medical Correspondent for CNN, in a radio post on June 9, 2014. Participants are then given an example of an outbreak investigation from Saudi Arabia in 1979 and asked to discuss how two-way tables could be used to organize data and determine the attack rate for each food item.
From the attack rate, students determined a relative risk for each food and also calculated which food had the highest relative risk. In this case, the meat was the cause of the foodborne outbreak.
Participants then recorded their results the following handout to tabulate the data for each food item based on who ate or didn't eat the food and who was sick or not sick afterward.
After all data had been collected per table, participants collected the whole group data using larger chart paper.
After the group collected all data, they calculated the attack rate for those exposed and not exposed to each food item by taking the total number of those sick and dividing it by the total within the exposed row and the not exposed row. Then, participants used these two rates to determine the relative risk by dividing the attack rate of those exposed by the attack rate of those not exposed. Finally, participants analyzed the data to determine which food was the contaminated food. Towards the end of the task, participants discussed how the simulation could be used across all grade levels. For example, elementary students may count to collect the data and use fractions and decimals when creating their attack rates. Middle school students can focus on rates, fractions, decimals, percents, proportions, and two-way tables. Further, high school students could analyze two-way tables with joint and marginal frequencies, statistical significance, confidence intervals for estimates, p-values, and causation versus correlation. This task may also be tied in other related events. In one example, power outages caused by inclimate weather are related to food poisoning prevention. Students learn that placing a frozen mug of water with a quarter on top is an excellent tool to determine when refrigerated food is no longer safe for consumption. During a power outage, the water melts and the quarter slowly sinks to the bottom of the mug. As the quarter's movement to the bottom of the mug provides an interesting measurement of time. When the quarter reaches the bottom of the bottom of the mug, it becomes clear that the refrigerated or frozen food may no longer be suitable to eat. Disease outbreaks and the CDC are another an interesting context for this activity. For example, there is concern about certain romaine lettuce and eggs, so we shared the information from the CDC in relation to these outbreaks. These warnings could be used to ignite a conversation about food poisoning in class, and thus more deeply contextualizing this topic of mathematics for students. (Some examples are provided below.)
Using fractions as operators means applying
fractions to numbers, objects, or sets as if they are themselves
functions (Behr, Harel, Post, & Lesh, 1993). Studies suggest
that deep understanding of fractions as operators supports
students' flexible reasoning with fractions in later mathematics
(Behr et al.,1993; Hackenberg & Lee, 2012). The operator
construct, however, seems easily forgotten in school curricula
(Post et al., 1993; Usiskin, 2007). We implemented tasks
intended for 7th-grade students in a class of K-8 preservice
teachers to elicit their thinking on fractions. We used tasks
across a unit to intentionally provide preservice teachers with
opportunities to encounter situations in which fractions can be
used as operators and to use fractions as operators in their
problem-solving. Selected student strategies for each task show
a variety of approaches utilized by students in their
problem-solving.
Figure 1. Task 1: An Incredible Discount We designed Task 1 to provoke student thinking through the use of fractions as operators; that is, solving the task involves applying a fraction (e.g., the final cost is 30% off the sales cost) to a fractional amount (e.g., the sales cost was 30% off the original cost). We subsequently chose student samples of incorrect solutions (see Figure 2) to illustrate different levels of problem-solving strategies and misconceptions. Student Strategies to Task 1: An Incredible Discount
Figure 2. Student Strategies to Task 1: An Incredible Discount Student 1's strategy, adding percentages, reveals a common misconception in which the fractional amounts (of different wholes) are simply added and subtracted from 100%. Student 3's and Student 2's strategies show a slightly higher level of reasoning in that they understand that multiplication is necessary, but incorrectly connect the product to the context of the task. That is, both fail to recognize the product as a "percent off" or difference. Although both are on the right track, Student 3 should subtract 21% from 70%. Student 2 adds 21% to 30% (the percentage off the original price) but should subtract 51% from 100%. Hence Student 2 finds the "percent off" the original price rather than the "percent of" the original price. Among these four students, Student 4 shows the highest and most valid fractional reasoning. He reaches a correct number but does not utilize formal notations and correct units. Task 1 (Figure 1) entails a composition of operations and is an example of using fractions as operators. So what does "fractions as operators" really mean and why should we emphasize this concept with upper elementary and middle grades students? Fractions As Operators: What Does It Mean? Five fraction constructs are recognized in mathematics education: part-whole, measurement, division, operator, and ratio (Behr et al., 1983). While the part-whole construct is an effective way to develop initial fraction understanding (Cramer & Whitney, 2010), previous research emphasizes that various fraction meanings introduced in later instruction improve fraction understanding (Clarke, Roche, & Mitchell, 2008; Lamon, 2012; Siebert & Gaskin, 2006). Behr and colleagues (1993) suggested that understanding fractions as operators can strengthen students' grasp of fraction multiplication, and also lead students' to translating word problems into number sentences more easily. Connecting algebraic thinking to understanding fractions as operators supports students' writing equations to represent multiplicative relationships between two unknown quantities (Hackenberg & Lee, 2012). Nonetheless, the operator construct often lacks emphasis in school curricula (Post et al., 1993; Usiskin, 2007). Evidence of students' understanding the operator interpretation of fractions includes students ability to: (a) interpret a fractional multiplier in at least two ways, (b) use one fraction for a composite operation, (c) relate outputs and inputs, and (d) identify a single composition of compositions (Lamon, 1999 and 2012; Marshall, 1993). We describe the four skills briefly. Lamon described (a) as thinking of a fraction (e.g., 3/4) in two ways: as multiple copies of one fractional part of the unit (e.g., 3 of [1/4 of the unit]) or as a fraction of multiple copies of the unit (e.g., 1/4 of [3 units]). In using (b), Lamon explained that students could use a fraction to describe a composite operation; that is, a fraction used to multiply or divide can be thought of as two operations performed as one. For example, multiplying a unit by 3/4 is the same as dividing the unit by 4 and then multiplying by 3. The third skill that students need, (c), is to understand the relationship between input and output: For example, a 3/4 operator defines a 3-for-4 exchange, transforming an input quantity of 4 into 3. Finally, Lamon described (d) as, for example, recognizing that 3/4 of (4/5 of a unit) is precisely equal to 3/5 of a unit. So how do we help improve students' understanding of fractions as operators? Enhancing Understanding Fractions as Operators For the brevity of the paper, we will focus on the first (a) and last (d) skills described in the previous paragraph. To help students interpret a fractional multiplier in more than one way, we first gave them the following task (Figure 3):
Figure 3. Task 2 To obtain the answer for Task 2, students typically partitioned this distance (3 miles) into three equal groups, resulting in a quantity of 1 mile in each group. Their answers came from taking two groups of 1 mile. Hence, 2/3 of 3 miles is 2 miles. As shown in Figure 4, while each of the four students represented three individual groups, they thought about it differently: Students 5 and 7 used diagrammatic representations, while Students 6 and 8 used graphical representations.
Figure 4: Student Strategies for Task 2 While the strategies in Figure 4 are common for this task because the context supports breaking three miles into three equal parts, there is another way of finding 2/3 of 3 miles to i
Figure 5. Alternative Approach to Task 2 Let us compare the strategies in Figures 4 and 5. In the student strategies (Figure 4), two-thirds of three miles is interpreted as two copies of one-third of three miles, or equivalently 2 x [1/3 x 3 miles]. In the second approach (Figure 5), the operation is interpreted as one-third of two copies of three miles, or equivalently 1/3 x [2 x 3 miles]. Students could also see that 2 x [1/3 x 3 miles] equals 1/3 x [2 x 3 miles] because of the commutative and associative properties of multiplication. Helping students see the connections between the approaches in Figures 4 and 5 might enhance their understanding of fractions as operators. In Tasks 2 (Figure 3), "2/3 of" is an example of an operator in which both multiplying and dividing may occur during the process of applying the operator. The result of a 2/3 of the operator, Jill's running distance, shortens the length because the operator does more shortening than lengthening. In particular, it lengthens Jill's distance by a factor of two and shortens it by a factor of 3. Whereas, in an example such as 5/4 of eight marbles, the 5/4 of operator increases the number of objects; that is, it does more increasing than decreasing because it increases by a factor of five and decreases by a factor of four. Thus, understanding fractions as operators means knowing a result of applying an operator such as 2/3 of three and 4/5 of eight can be decreasing or increasing, which will help address the misconception that multiplication "always makes bigger" and division "always makes smaller" (Clarke, Roche, & Mitchell, 2008; Karp, Bush, & Doughtry, 2014). A Composition of Compositions After our students completed Task 2 and we discussed connections between alternative strategies for the task, we asked them to complete Task 3 so that we could explore their understanding of fractional operators with regard to the commutative property. Task 3 was adapted from Beckmann (2014) and is shown in Figure 6.
Figure 6. Task 3 Two student strategies were selected and are shown in Figure 7. Both Students 1 and 3 (Figure 2) complete Task 1 incorrectly but solve Task 3 correctly. Student 3 multiplies the two percentages as she does in Task 1, but this time she correctly multiplies the first time and second time marked-up/marked-down price percentages and provides correct answers with units included. Student 1 incorporates all the operations correctly and in the correct order. Additionally, Student 1 displays a more detailed written description of her reasoning, which indicates some substantial improvement in her/his conceptual understanding of percentages. This is in contrast to the understanding we observed in Task 1, in which she considers the result of a sequence of percentage changes as a result of an addition operation.
Figure 7. Student strategies to Task 3 Conclusion Understanding fractions as operators should not be forgotten in school curricula. Through the implementation of these tasks, students were exposed to situations in which fractions were used as operators and used fractions as operators in their problem-solving. When working on Task 3, students were also able to write equations representing a multiplicative relationship among quantities, which supports findings from Hackenberg & Lee (2012)'s study that understanding fractions as operators can support students in writing equations to represent multiplicative relationships between quantities. With a goal of exploring variations of student problem-solving strategies and enhancing student understanding of fractions, we encourage teachers to implement these tasks and share student solutions and discussions. Fostering students' reflection about making sense of their problem-solving strategies through discourse supports the type of deeper understanding that we want our students to have. References Beckmann, S. (2014). Mathematics for Elementary Teachers with Activity Manual. 4th ed. New York: Pearson. Behr, M., Lesh, R., Post, T. & Silver, E. (1983). "Rational number concepts." In R. Lesh and M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, pp. 91-125. Academic Press, New York. Behr, M. J., Harel, G., Post, T. R. & Lesh, R. (1993). "Rational numbers: Toward a semantic analysis--emphasis on the operator construct." In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational numbers: An integration of research, pp. 13-47. Hillsdale: Lawrence Erlbaum Associates Cramer, K. A., & Whitney, S. (2010). "Learning rational number concepts and skills in elementary classrooms: Translating research to the elementary classroom." In D. V. Lambdin, & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom, pp. 15-22. Reston, VA: NCTM Clarke, D., Roche, A., & Mitchell, A. (2008). 10 practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(7), 373-380. Hackenberg, A. & Lee, M. (2012). Pre-fractional middle school students' algebraic reasoning. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky (Eds.), Proceedings of the 34th annual meeting of the north American chapter of the international group for the psychology of mathematics education, pp. 943950. Kalamazoo, MI: Western Michigan University Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21(1), 18-25. Lamon, Susan J. (2012). Teaching Fractions and Ratios for Understanding. 3rd ed. New York: Routledge. Lamon, Susan J. (1999). Teaching Fractions and Ratios for Understanding. Mahwah, NJ: Lawrence Erlbaum Associates. Marshall, S.P. (1993). "Assessment of rational number understanding: A schema-based approach." In T.P. Carpenter, E. Fennema and T.A. Romberg (eds.), Rational Numbers: An Integration of Research, pp. 261-288. Lawrence Erlbaum Associates, New Jersey. Post, Thomas, Kathleen Cramer, Merlyn Behr, Richard Lesh, and Guershon Harel. (1993). "Curriculum Implications of Research on the Learning, Teaching, and Assessing of Rational Number Concepts." In Rational Numbers: An Integration of Research, edited by Thomas Carpenter, Elizabeth Fennema, and Thomas Romberg, pp. 327-61. Hillsdale, NJ: Lawrence Erlbaum Associates. Siebert, D., & Gaskin, N. (2006). Creating, naming, and justifying fractions. Teaching Children Mathematics, 12(8): 394-400. Usiskin, Z. (2007). Some thoughts about fractions. Mathematics Teaching in the Middle School, 12(7): 370-373.
When asked to name the most hated subject in school...mathematics often wins. Why, I ask myself, is something so basic and necessary in life, so despised? Could it be that math is perceived as boring? Tedious? An un-necessary evil? Possibly. I postulate that math is not only, necessary, but it is anything but evil. So, let's look at the adventure that is mathematics.
Editor's Foreword:
As she shared her success of the following lesson through social media, the creative and mathematical nature of her lesson struck a chord. (Pun intended, Geometry folks.) Through the promotion of early mathematical vocabulary, creativity, and navigation, this STEAM lesson illustrates that the field of mathematics is not mutually exclusive with other disciplines. Mathematics can be used to make other subjects interesting and engaging. Although Mrs. Hong may differentiate this activity with most elementary grade levels, I challenge our readers to think about how they could use the lesson in their classroom. Could this activity be used to discuss relationships between inscribed angles, cyclic quadrilaterals, or even trigonometry? Could instructors vary the circle size or have a different number of notches along the perimeter for students to explore? Think of how you and your students could use cardboard circles and string to explore mathematics! And, if you do branch off and adapt this lesson for your classroom, don't forget to let us know how it goes. We would love to hear from you. Have fun! Fourth/Fifth Grade Art: String Art and Geometry - 3 (45 minute) sessions required
Power Standard(s):
Essential Question(s):
Vocabulary:
Instruction: Day 1:
Closing of Day 1: Conduct a brief critique of the work done today. Collect all the work and use the document camera to show the various patterns that were created today. Discuss what worked well and what could use improvement. Explain that we will be recreating our best patterns with tag board and yarn during the next art session.
Closing Day 2: Discuss our goals for the next session and any problems we may have encountered during today's session. Day 3:
Closing of Day 3: Conduct a brief critique of student artwork. Which designs catch your eye and why? Does craftsmanship play a role in the success of the work? Do you feel like you have a better understanding of geometric shapes and patterns? Do you feel like you have a better understanding of the markings on a compass or a clock?
Struggling scholars will start with simple shapes and practice until they feel comfortable. Advanced scholars will explore more complex patterns, possibly using more than one color string to enhance the design. Technology/Resources: smartboard, laptop, and document camera will be used for instructional purposes Formative Assessment: Verbal assessment in the form of questions and discussion. Visual assessment of sketches and artwork. Summative Assessment: Scholars will be assessed based on a standard rubric, which takes into consideration the goals met (Did the student create at least 4 sketches? Did the student create at least 2 string art designs?) and craftsmanship.
GCTM would like to congratulate 2017's award and grant recipients. As a GCTM tradition, these recipients were recognized at the 2017 GMC. Click here to download a Powerpoint of the GCTM 2017 awards presentation.
Do you know a teacher of mathematics that
goes above and beyond their job description to assure their
students are successful? Now is the perfect time to stop and
recommend this person for a well-deserved GCTM honor/award. The deadline for nominations for the following awards is Labor Day of the current year.
GRANTS
Click here to find out more!
Before we know it, mathematical educators across the state will be making their trek to Rock Eagle for the Georgia Mathematics Conference. GMC 2018 will host inspiring speakers and offer engaging sessions to help refresh and renew your professional perspective this Fall. Click on the image below to learn more about this year's keynote speakers. There will be so much to explore, that you will likely want to come for all three days. Check out the Conference Overview.
Here are just a few images from our GMC 2018 Scrapbook.
Why don't you join us? Better yet, consider being a speaker. Complete the speaker form present your own lesson. We can't want to see you!
NCTM continues to recommend that "High School mathematics should discontinue the practice of tracking teachers as well as the practice of tracking students into qualitatively different or dead-end course pathways." Therefore, encourage this change, NCTM also offers a plethora or resources to address making mathematics more accessible, promoting equity in the classroom, and empowering students through mathematics.
Your NCTM membership includes access to resources, new networking opportunities via email and discussion boards, and chances to professionally grow through various national conferences. Continue renewing your membership today!
Summer Means Renewal
As you RENEW, please put GCTM RENEWAL on your list! $20 will continue to bring you the benefits of GCTM and enrich you and your students. Think of how often you go through a drive-through and spend $10 or more. GCTM uses your membership fees VERY wisely, and we appreciate your loyalty. We need you! Drive through to GCTM today! Our membership count stands at 1245! | There are 457 lapsed members in 2017.
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Table of Contents President's Message - by Bonnie Angel, GCTM President Advocacy Update - by T.J. Kaplan, Advocacy GCTM Middle School Math Tournament News - by Chuck Garner, VP for Competitions GCTM State Math Tournament News - by Chuck Garner, VP for Competitions Have You Ever Had Food Poisoning? - by Ashley Cody and Michelle Mikes Fraction as Operator: Not Forgotten by Ha Nguyen, Heidi Eisenreich, Eryn Stehr, and Tuyin An Why Hate Math? by Sybil E. Coley, Retired Math Teacher Fourth/Fifth Grade Art: String Art and Geometry by Sun Hong NCTM Report - by Michelle Mikes GCTM Membership Report - by Susan Craig, Membership Director
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Georgia Council of Teachers of Mathematics | PO Box 683905, Marietta, GA 30068 |
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k, where k is a positive integer. Compute
k.
Mrs.
Coley is a retired math teacher who taught high school and college
mathematics in both private and public institutions including
Woodward Academy. While at Woodward, Mrs. Coley received the
Presidential Award For Excellence in Mathematics and Science
Teaching. Although she has taught topics from Algebra through
precalculus, she adores teaching Geometry. Currently residing in
Woodstock, Georgia, Mrs. Coley enjoys spending time with her five
grandchildren, traveling, and writing poetry.
Sun
Hong, a Cobb County School District Elementary Art teacher,
submitted the following lesson plan. She has been a sweet friend
of mine since middle school, and somehow we both found ourselves
enjoying our professions in this wonderful world of education.
While our students and content areas are quite different, our
passion for education remains the same. 
Day
2:
Differentiation:
As
we move into a slower pace and some personal time, being a teacher
also means a time of renewal. Teacher summers are always busy, even
without the daily planning for classes. You might find yourself
taking graduate courses, planning for the upcoming year, or revising
lessons used in the past. It is still a busy time, but one you can
control better than during the academic year.