Instead of discussing moral purpose as a teacher (in general), I would like to reveal my moral purpose as a mathematics teacher. You would think they are similar, but I would like to point out that they are not. I have tried for years to find a resource out there online that mirrors my own moral purpose, and I believe I’ve stumbled upon one by pure chance. It is articulated in a paper that was written by Mevarech and Kramarski titled *Critical Maths for Innovative Societies: The Role of Metacognitive Pedagogies*. Described in the first chapter is what I have been trying to share with math colleagues for years.

“Problem solving is at the core of all mathematics education. The solution of complex, unfamiliar, and non-routine (CUN) problems has to be the cornerstone of any effective learning environment for mathematics for the 21st century. … Mathematical reasoning, creativity and communication are essential components for solving CUN problems. Developing these competencies should not be limited to gifted students or high level grades. On the contrary, they can be applied in all age groups and should be the cornerstone of any effective learning environments.” (2014)

In my opinion, the key phrase is “complex, unfamiliar, and non-routine problems.” The chapter then describes what I have known for years. In traditional texts, story problems are made to utilize the new concept being taught and requires limited knowledge to solve. In fact, most of the problems are not even realistic. I am terrible at describing and sharing my personal thoughts, and so this is my new moral purpose for mathematics education.

So what strategies do I use, and how are they related to my leadership? First off, I need to make sure that what is being described in this paper doesn’t contradict our curriculum, and is in alignment with national authorities making recommendations about math education. According to our Alaska Mathematics Standards from DEED, “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” (2012) I have some issues with the word “can” in this sentence. It should state “will”. To me, “can” implies they would be able to, but makes no assertion that it will happen. A little nitpicky, I know, but it doesn’t contradict this new CUN problems idea, which is excellent. (Note: I did not see any wording or implications about CUN type problems in the State Standards) The National Council of Teachers of Mathematics states “Beyond showing the relevance of mathematics in an array of careers, you should also emphasize its practical value in offering approaches to real problems.” (2009) Again, an emphasis is on real problems, which is great. I have a little issue with the word “value”, but no contradictions thus far. (Note: Again, I didn’t find any reference to doing CUN type problems either.)

Second, now it is a matter of making sure I utilize some CUN problems in my own class if I am to convince other math teachers of the benefits of this approach. Teaching statistics lends itself a little to CUN problems. There is data everywhere and how we analyze it can be applied to real world data. In fact, the textbook I use for the class is filled with real world data. Citations abound and researchers are duly credited.

Lastly, I need to show that having students solve these CUN problems will actually assist them in their ability to show competence in passing standardized assessments that are required in K-12. It might take a few years to see the accomplishments of this new pedagogy, but I do believe that it will increase achievement in the long run.

Fullan describes how if leadership is to be effective, it has to

“(1) have an explicit “making-a-difference” sense of purpose, (2) use strategies that mobilize many people to tackle tough problems, (3) be held accountable by measured and debatable indicators of success, and (4) be ultimately assessed by the extent to which it awakens people’s intrinsic commitment, which is none other than the mobilizing of everyone’s sense of moral purpose.” (2001)

I may not have addressed all these qualities, but it would be my goal in leadership to make the new moral purpose sustainable and succeed in improving students abilities in tackling complex, unfamiliar, and non-routine problems in their lives.

References:

Alaska Mathematics Standards. (2012) Department of Education and Early Development. [PDF]. Retrieved from https://education.alaska.gov/akstandards/math/akstandards_math_081312.pdf

A Teacher’s Guide to Reasoning and Making Sense. (2009). National Council of Teachers of Mathematics. [PDF]. Retrieved from http://www.nctm.org/uploadedFiles/Standards_and_Positions/Focus_in_High_School_Mathematics/FHSM_TeacherGuide.pdf

Fullan, Michael. (2001). *Leading in a Culture of Change*. John Wiley and Sons, Inc. [PDF]. Retrieved from http://files.eric.ed.gov/fulltext/ED467449.pdf

Mevarech, Zemira; Kramarski, Bracha. (2014) “Mathematics Education and Problem Solving Skills in Innovative Societies”, *Critical Maths for Innovative Societies: The Role of Metacognitive Pedagogies*. OECD Publishing, Paris. DOI: http://dx.doi.org/10.1787/9789264223561-en

I enjoyed reading your math perspective to the class question and how you use this in your moral purpose. The CUN problems are new to me but I like how it is focusing on training students to “think about their thinking” during learning. Do you see a lot of struggle when they shift from routine problems to complex, unfamiliar and non-routine problems? I can see that learning these strategies could benefit not only their standardized testing but for life long application as well. I think learning to analyze real world data would be more beneficial than using those ready-made algorithms. You are right, data is everywhere. We should use it to help our students think critically.

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I think CUN problems are the essence of mathematics in real life. I think we do students a disservice if we don’t give students opportunities to solve these kinds of problems, and yes, they struggle. Only because they are used to “instant recipe” problems. They are given the necessary information, and usually not extra, so it’s not too difficult to solve them. We need to challenge students more than this.

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It is so true that many students lack problem solving skills. I have found that it is hard to teach any of these problems without basic math skills that do require memorization for the most part. I have taught pre-algebra and algebra, and this semester I am teaching 8th grade math. My students are struggling because they don’t have their basic math facts down to solve more complex problems. These students are very low mathematically and if I through even a simple word problem into the mix they won’t try it. I think a lot has to be built up. I love hands on equations because it has word problems that go along with basic equation solving. This has really helped my students to be able to try some simple problems. I have also been trying to do more math in physical science. Almost all of these are word problems that require some thought as to how to use the information given. I think this for students seeing math in 2 classes is helping some to realize that math is in many places and not only in math class. I definitely think that once basic math facts are more readily recalled students should be pushed to try new problems. They need to learn to be creative and that not everything is done the same way.

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