Mathematics Updates
February 2017
Research-based Strategies for Test Prep
Making students aware of the progression of expectations in the achievement level descriptors can help reduce some of that anxiety. An awareness of expectations can boost students' understanding of what they need to be able to do in order to show what they know.
Studies done on the effects of testing indicate that it is a powerful means of improving learning, not just assessing it. The most effective learning strategies include the following:
- Practice testing - forces recall of information and indicates what content needs to be restudied
- Distributed practice over time - spirals back to previously practiced content
Other strategies that show promise but need further research include these techniques:
- Interleaved practice - a practice that involves distributed practice but also mixes up the order of the content over different topics
- Elaborative interrogation and self-explanation - making connections to previously learned information and explaining how and why
Read the article by John Dunlosky to learn more about these strategies.
_________________________________________________
Technical College Readiness Mathematics FAQ Update
As a result of feedback from the State Mathematics Advisory Council, GaDOE has revised the Technical College Readiness Mathematics FAQ document for enhanced clarity. In particular, statements regarding matriculation to USG institutions have been clarified in answers to questions 16 and 18.
The revised version has been posted at GeorgiaStandards.Org. If you have a paper copy of the FAQ document, please note that the first version has a footer date of January 5, 2017, and the revised version shows January 17, 2017, in the footer.
_________________________________________________
Thinking Algebraically: From Elementary to High School
From NCTM Research Briefs
Research has begun to shape both our ways of conceptualizing algebraic thinking and the routes by which its growth might be encouraged. Three of its main themes are thinking relationally about equality, thinking rule-wise in pattern generalization, and thinking representationally about the relations in problem situations.
- Children who view the equal sign relationally do not need to compute the total of both sides of an equation such as 67 + 86 = 68 + 85 in order to determine equality. Research has shown that viewing the equal sign relationally is indicative of algebraic thinking and moreover supports more advanced forms of algebraic activity.
- Recent research in patterning suggests that pattern generalization is algebraic when it involves generating rules to calculate with. Once children have determined the commonality of a pattern and have generalized it to other terms, an effective question to ask them is how to build a really "big" figure of the sequence, without specifying a particular figure number.
- Elementary school children use a variety of representations to signify the relations in the mathematical problems they are asked to solve-some of these representations providing a potential bridge between arithmetic and algebra. The so-called pictorial-equation method is one representation that has been found to be especially conducive to developing algebraic thinking.
Recent research in algebra teaching and learning has included a focus on the solving of word problems and the activity of conjecturing and proving. In many studies of the ways in which algebraic reasoning can be fostered in these two areas, specific attention has been given to the role of teacher questioning. In the area of conjecturing and proving in algebra, research has also emphasized the need to support such activity with appropriate tasks where students engage in higher-level reasoning processes such as reflecting, explaining, and justifying.
- To promote algebraic reasoning in solving word problems, an effective practice is to include within a table-of-values representation not only the numerical values associated with the given variables of the problem, but also the numerical equation calculations that yield each of these values. Comparing different equation calculations for arriving at the same values can lead students to see that some calculations are more generalizable than others.
- Research suggests that generic proofs merit much greater attention in algebra teaching practice than they currently receive. As well, engaging in proving tasks needs to be preceded by significant activity on developing the related reasoning processes of predicting, comparing, explaining, and conjecturing.
Read the entire research briefs:
_________________________________________________
College STEM Courses Boost HOPE GPA
The courses currently approved are ones required to obtain a major leading to one or more of the STEM career fields that require at least a bachelor’s degree and are considered to be in high demand in Georgia. The University System of Georgia (USG), the Georgia Independent College Association (GICA) and the Technical College System of Georgia (TCSG) worked collaboratively, along with input from the Georgia Department of Economic Development regarding high demand careers, to draft an initial list of rigorous STEM courses eligible for weighting.
To view the complete list of approved courses, please visit www.GAfutures.org. For additional information, students should contact their HOPE-eligible postsecondary institution.
_________________________________________________
Videos of Lessons and Strategies from Teaching Channel
Grades 3-5
Grades 6-8
_________________________________________________
Ten Suggestions for Reducing Stress
Research ranks teaching as one of the most stressful professions. In addition to the stresses of work, less daylight during winter months can create subtle negative issues. Add to that, testing season is approaching. Preparing students to do well on state tests can trigger further anxieties. With all these conditions upon us, it is important to consider ways to get rid of the stress that can build up. The stress-reducing tips listed below are lifted from a blog by Vicki Davis.
- Acceptance. List the worst thing that can happen. Go ahead and accept the worst. Then, start improving it.
- Interrupt negativity. Your thoughts create a mental momentum that spills over into your physical world. Part of self-awareness is the ability to pull back and observe your thoughts from a distance. Interrupt negative thoughts and replace them with positive ones.
- Keep a joy journal. Looking for joy is like looking for a color. When you look for the color blue, you see it everywhere. Start noticing and writing down things that bring you joy. You’ll re-set your mindset and become happier.
- Make time to sleep. Set an evening alarm to remind yourself that it is time to go to bed. Sleep loss makes it harder to think, harms your health, and worsens your mood. It can even make you gain weight. Put sleep on your schedule and aim for seven to eight hours a night.
- Drink enough water. Take time to drink water. The effects of dehydration are real and especially detrimental to those who must stay positive and think clearly. Keep a container of water close by, and make drinking water part of your habits.
- Exercise outside. Sitting is the new cigarette. Every 90 minutes a human needs to move. Just five minutes of exercise gives you a positive mood-boosting rush. Exercising outdoors will boost your mood even more.
- Have faith. Research-proven ways of handling stress include meditation, deep breathing, aromatherapy, listening to music, visualization, and prayer. A strong correlation exists between religion and positive mental health.
- Relate deeply. As humans, we need intimacy. Gossip and negative talk about problems can bring you down. Mutual enjoyment and common pursuits can lift your spirits. Develop relationships and improve your life.
- Touch others. Physical touch reduces stress. Appropriate physical touch can boost your mood and the mood of those around you.
- Unplug and recharge. Constant interruptions can make you feel like a human doing and not a human being. Stop using electronics one hour before bedtime. Recharge devices away from your bedroom. Set “do not disturb” times during your week to get away from technology.
_________________________________________________
Math Professional Learning in February
February 6, 2017 - Madras Middle - 4pm - 5pm
Ideas Worth Sharing: Preparing Students for the Milestones
With testing season right around the corner, the district-wide Middle School Math meeting will focus on tips and strategies for helping students be successful on the Georgia Milestones. Participants are asked to bring their Chromebooks. No registration is required.
February 13, 2017 - K-2 Math Webinar - 3pm - 4pm
Developing Number Concepts: Addition and Subtraction (Part II)
This is the second of a three-part series of sessions. A variety of teacher-directed and independent activities focused on helping children interpret and symbolize addition and subtraction will be discussed in this session designed for teachers of Kindergarten through Grade 2. Register by 4 p.m. on February 10 at https://goo.gl/forms/x2ajMhchRFvWZGEM2 to receive an invitation to join this session.
February 16, 2017 - 3-5 Math Webinar - 3pm - 4pm
Fractions and Decimals (Part III)
In this third of a series of sessions, use of manipulatives will be explored to help build students’ understanding of operations with fractions and decimals as they move toward standard algorithms. This session is designed for teachers in Grades 3-5. Register by 4 p.m. on Feb. 15 at https://goo.gl/forms/OFTJGP3YrsKAcpAm2 to receive an invitation to join this session.
_________________________________________________
Research Base
Brown, P., Roediger, H., & McDaniel, M. (2014). Make it stick: The science of successful learning. Cambridge, MA: Harvard University Press.
Dunlosky, J. (2013). Strengthening the student toolbox: Study strategies to boost learning. American Educator, 37(3), 12-21. Retrieved from https://www.aft.org/sites/default/files/periodicals/dunlosky.pdf
Georgia Department of Education. (2015). Georgia Milestones Achievement Level Descriptors, End-of-Grade and End-of-Course resources. Retrieved from http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/Georgia-Milestones-ALD.aspx
Karpicke, J.D., & Roediger, H.L. (2006). Repeated retrieval during learning is the key to long-term retention. Journal of Memory and Language, 57, 151-162.
NCTM. (2014). Algebraic reasoning research brief: What does research tell us about fostering algebraic reasoning in school algebra? Reston, VA: Author.
NCTM. (2014). Algebraic thinking research brief: What does research tell us about fostering algebraic thinking in arithmetic? Reston, VA: Author.
Wolfe, P. (2010). Brain matters: Translating research into classroom practice. Alexandria, VA: ASCD.