Balanced Mathematics Facilitator Notes

Slide Title Purpose Notes The question – what can we do to improve mathematics teaching and learning in the state of Utah? The common core will help, but unless instruction in the Balanced Mathematics classroom changes and Slide 1 Introduction – What is it? the beliefs of students and teachers change we will not make much progress. A program of Balanced Mathematics along with the core shows promise of making that difference. Slide 2 Context What is the current Bullet 1: Internationally, situation in on every mathematics mathematics teaching test comparing us with and learning nationally other nations, the US and around the state? ranks in the low range of mediocre. While other countries have been using ideas that mostly originated in the US to improve their students’ achievement we have followed one failed cycle of reform after another.

Bullet 2: In her book Math: Facing an American Phobia, Marilyn Burns asserts that two thirds of American adults fear and loathe math. That fear is being passed on to their children – your students.

Bullet 3: STEM careers are those that deal with Science, Mathematics, Technology, and Engineering. The United States has led the world in these disciplines for many years. However, in 2005 the Business Roundtable estimated that if current downward trends in students entering STEM programs in colleges and universities continues, 90% of all those in STEM careers will live in Asia.

Bullet 4: Math Wars – for years there has been a tug of war between those who believe that mathematics should be taught directly and explicitly (the procedural, algorithm first approach) and those who believe students must be taught to understand mathematics conceptually (the conceptual approach). Besides being distracting and a nuisance, the math wars have led to continuing changes in math curriculum over the years. More on that later. Slide 3 Our Secret Weapon Teacher Character and Self-explanatory – be Dedication can make sure to emphasize that the difference. in many studies the most important factor in student learning and achievement in classrooms is the effectiveness of the teacher – not the preparedness of the students, or their economic or ethnic background. And we have great teachers in Utah Let the participants listen to Billy sing for a while until after he sings “I go to extremes” then discuss with them Entertaining Intro to the dangers of Slide 4 Pendulum Swings swings back and forth in pendulum swings – the curriculum confusion, a lack of focus, a lack of coherence, a helter skelter searching for the “best” textbook Slide 5 Balance Compare balanced Bullet 1: For years we literacy with the went back and forth promise of balanced between direct, explicit numeracy – balanced teaching and whole mathematics. language approaches in literacy instruction until some very smart people decided to stop going to extremes and meet in the middle. They created balanced literacy which contains elements of both extremes. You must do some instruction directly and explicitly while other instruction can be done in a spirit of exploring, inquiring about, and interpreting literature and informational text.

Bullet 2: Can we do the same thing with mathematics? Can we create balanced numeracy in our state. Can we balance direct explicit instruction and learning basic skills with inquiry learning and make it work for all students, ensuring that they ALL get an excellent education in mathematics. The answer is Yes, we can. That is what the Core Academy is all about. That is what the Utah Core State Standards in Mathematics are all about. Slide 6 So what are we What elements of math Bullet 1: The type of balancing? instruction need to be math learned needs to balanced? include both elements. It is very important for students to understand the ideas of mathematics – the concepts. It is also important to know the procedures, the ways of getting an answer. You don’t want students counting on their fingers or carrying hundreds flats around with them their whole lives. So, balance is the key. Bullet 2: The type of teaching needs to fit the situation. Sometimes you need to directly teach something (notation comes to mind) and sometimes inquiry is the right way to go. Balance them, and students learn more. Bullet 3: Do you want students to learn to use a process or to get a product? Both. Processes are very important, but they need to be balanced with products. We don’t get very far if we never produce anything. In mathematics, products are answers to problems. Processes are how you get there. Bullet 4: Our students have been led to believe that there is only one right way to get an answer. In reality, there are many ways. Students need to see and experience multiple strategies for getting answers so they can learn to persevere – which is part of Practice Standard 1. Bullet 5: Assessing mathematics processes and products requires more than what we might do traditionally (assessment of learning) (ask what some of those ways are – tests, quizzes, assignments, are the most likely answers). Formative assessments, those we do constantly all the time, also have a very important place. What are some ways to assess for learning? Bullet 6: Discourse patterns – teacher to student, student to teacher, student to student. All are important, but be sure there is a hefty dose of student to student interaction. Students learn from each other when mathematics becomes a social activity instead of something we do all alone at our desk or in our cubby – or our paper office. Bullet 7: Practice – different purposes of practice. Practice during discourse allows students to firmly grasp the concepts as students discuss them together and with the teacher. Practice in isolation allows the student to be sure s/he knows the concepts/procedures of him/herself. Most practice should be during discourse, but it should be balanced with some time for isolated practice. Bullet 7: Unlike some programs that ask for students to find an application for the learning after they have learned the concept, we believe that learning the concept in an application, with a real context is more generative and more powerful. That is why we use math tasks to introduce a concept. We continue to use tasks throughout the learning process until we know that students have solidified their understanding. We may ask them to create their own context as a means of determining their level of understanding. Go through the points Help teachers see that Beliefs of a traditional one by one. Pretty self- we have been following Slide 7 approach to math explanatory. Be sure to traditional math teaching take questions and teaching forever. comments. Go through the points How should we balance one by one. Pretty self- NCTM Principles and Slide 8 learning procedures and explanatory. Be sure to Standards learning concepts? take questions and comments. Go through the points Beliefs that lead to a one by one. Pretty self- Concepts before Slide 9 Balanced Approach to explanatory. Be sure to procedures Teaching Math take questions and comments. Slides 10 and 11 Related Issues in What can we learn from These slides can be Balanced Literacy balanced literacy that particularly powerful will help us with for elementary balanced mathematics? teachers, most of whom understand balanced literacy very well. Be sure to tie what is on the slides to mathematics instruction. Many of the problems we have with inquiry learning come from just doing inquiry and never tying it to real mathematical learning. Yet, we have to have students explore the math in order to learn the concepts AND to learn to love and appreciate mathematics – and have fun with it. Just don’t go to extremes. Don’t do EVERYTHING directly, and don’t do EVERYTHING by inquiry/discovery. Read Dr. Ball’s Dr. Ball is the leading statements and then authority on teaching discuss them. Deborah Loewenberg Slide 12 and learning Mathematics Ball mathematics in instruction can and elementary school. should take many different forms. Go through the points What else do you one by one. Pretty self- believe that allows you Slide 13 Other beliefs explanatory. Be sure to to balance take questions and mathematics? comments. We will be focusing on inquiry mathematics in this course but not because we want you to go out and do everything as an investigation. As we try to balance mathematics instruction, we need to take the direct teaching that most of you are doing and turn it on its What does inquiry in a head. We need to start Slide 14 Fundamental Inquiry mathematics classroom with the inquiry so that look like? students learn the concepts and then do some direct instruction to help students with notation and with the finer points, such as standard algorithms. Go through each of the stages of the three part lesson design and discuss them. Launch – Explore - Discuss Slide 15 Inquiry Lesson Model What is the lesson cycle This is how you take the for inquiry math? three parts of an inquiry lesson and make certain that students develop enduring understandings of mathematics. 1. Self-explanatory 2. Self-explanatory 3. Self-explanatory 4. Self-explanatory 5. This is called the practice part of the cycle. 6. This is called the solidify part of the cycle. In this course we are going to focus on steps 1 through 4. They will help you understand how to use worthwhile mathematics tasks in your classroom. Conceptual understanding: we know that students know the ideas (the concepts) of mathematics and so they. They see how they are interrelated. Procedural Understanding: Students understand why the procedures What are the outcomes work and they know Elements of Balanced of a balanced Slide 16 how to use them to get Instruction mathematics answers to problems. classroom? Fluency: This means that students have skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. It does not equate with rote memorization. Students have mental math strategies that they can use to be fluent. Slide 17 Teachers in Transition Do you have to change 1. Most teachers everything all at once? now teach procedures directly. In other words, they teach the algorithm and then have students practice how to use it. They really don’t teach mathematical concepts. 2. In order to begin the change, teachers may start teaching some concepts directly, helping students to understand the “why” of mathematics while continuing to teach procedures as they have been. One means to this end is to ask students to justify their answers. Another is to use the principle of metacognition – thinking out loud – as you teach mathematics, explaining each step as you take it and why you are taking it and what is the mathematical reasoning behind it. 3. The next step would be to begin teaching concepts in an inquiry setting, using mathematical tasks, a few at a time while continuing to teach procedures directly. 4. The last step, and fully balanced mathematics, is to do it all. Teach concepts and procedures both directly and through inquiry, depending on student need. Teach concepts through procedures and procedures through concepts and mix direct teaching with inquiry. It can be done! We’ll see some examples this week Ask for questions and Slide 18 Questions, Comments Questions, Comments comments, and then be nice and answer them!