Run this slide while participants are coming in and getting seated.What is the Algebra Readiness course?What does a MIND Algebra Readiness class look and sound like?What’s so different about this curriculum that students who have never been able to do math before suddenly get it?!What mathematics is taught using the number line?What are the components of each lesson and why is each significant to student learning?How does the MIND Algebra Readiness course support me to guide ALL my students to mastery?ST Math: what is it? How do students use it? How do I facilitate their learning with it?What do I need to do to connect my students visual learning in the games with their abstract symbolic learning of mathematics?What resources are provided?
Time: minutes (8:00-8:10)Materials: noneTrainer’s Process and Focus Questions:Welcome, introductionsACTIVITY:Restroom locationsCell phones off or vibrate modeAsk questions as they occurLet participants know about the 2nd day of training. Today will learn about how to use al the components of the curriculum with an emphasis on the content in chapters 1 and 2. Second day will focus on rates, use of assessments to differentiate for the needs of your students. Both days will include ways to use the software component to increase student understanding and achievement.Let them know about the Teacher forum: an on-line Professional Learning Community
Time: 4 minutes (8:10-8:14)Materials: Computer with Rolling Equations, level 2 readyTrainer’s Process and Focus Questions:ACTIVITY: Play Rolling Equations, level 2. Share: When my students played this game, all of a sudden they were thinking, participating, and trying things that were difficult.My students who had a history of failure, may have poor work habits, lack in basic skills and number sense. My kids who said:“I always get bad grades in math.”“I don’t get it, especially fractions.”“I can’t remember all the steps. ”“I suck at math. I’m stupid.”“I’d rather they think I’m lazy than for them to know I’m stupid.”felt that they were smart. For some of them, this was the first time in a very long time that they felt smart in math.
Time: less than 1 minute (8:14-8:15)Materials: noneTrainer’s Process and Focus Questions:Teachers have been given the challenge to really make a difference with these students. Research consistently shows that it is the teacher, not the program that makes the difference.
Time: less than 1 minute (8:14-8:15)Materials: noneTrainer’s Process and Focus Questions:Share out statistics about struggling students.-Share this quote form Ed Week with participants: ‘Only 60 percent of the students who take algebra pass it. - Ed Week.org-More than 2000,000 students repeated the Algebra 1 CST in 2008http://www.edsource.org/data_RepeatAlgICST08.html-The way math is taught makes a difference in the transition to algebra. -Students need to understand basic math concepts in order to build a foundation for higher level mathematics. Once the foundation is built, students can continue their progression of math skills. -Per the National Mathematics Advisory report released March 2008: “Many students come to their first years of school unprepared. The level of math knowledge they bring to school affects their math schooling for years to come. Intervention programs are important in the early years to eliminate this gap.”-
Time: 2 minutes (8:15-8:17)Materials: noneTrainer’s Process and Focus Questions:Alternative approaches reach previously unsuccessful students. Doesn’t work to try to teach the same things in the same way.“I’ve already done this before in elementary. “Why do I have to do it again?”“I already know how to do this.”Story of doing task analysis, teaching to areas of need, students participating and then still making same mistakes.Share these research results:“In the 1940s, Canadian neuroscientist Donald Hebb was concerned about how, at the brain cell level of description, learning could become permanent in the brain. He proposed that wherever a pair of neurons were repeatedly stimulated together, this synaptic functioning of information transfer becomes more efficient. That is, repetition produces recall with less effort and more accuracy. More recently, studies of neuron physiology, and of the electrical activity of brain modules, have supported Hebb’s model (Changeux, 1985).”“This observation highlights two further implications of Hebb’s model for school teaching. The first is about the correction of errors. Reinforced neural pathways tend to stay that way. A well rehearsed mis-concept is unlikely to be altered by a simple red cross on a homework assignment. What is required is the reinforcement of an entirely new neural pathway to represent the correct concept. The music student who has conscientiously practised the wrong note needs much more practice to be put right than just a teacher’s passing comment.”ACTIVITY: Participants read Matthew’s letter to the students, p. xiii Highlight parts that might connect to your students. Pop Up- share one part that might connect well with where the students are.
Time: 5 minutes (8:17-8:22)Materials: video clip embedded in PPTrainer’s Process and Focus Questions:Dr. Matthew Peterson is an electrical engineer and a neuroscientist. In 1998, he co-founded a nonprofit research organization called the MIND Institute, which is dedicated to improving K-12 mathematics education. Dr. Peterson is the inventor of the ST Math software and author of all of the mathematics curricula at MIND Research Institute. Show part of the video where Mathew is talking about learning math visually, on our website. ACTIVITY: Shout out a number between one and ten. (hopefully someone says 3). Now tell me 3 things you saw in this clip that tell how the ST Math approach words.KEY POINTS:-Language, numbers and symbols are set aside until the conceptual understanding of math is developed.-Visual models are used.-Animation shows the mathematical consequences of the choice made.-Problems start out simple, and then progress in difficulty.Will spend time each of the training days exploring the software and learning how to connect it to the classroom instruction and the textbook.
Time: 1 minutes (8:27-8:28)Materials: noneTrainer’s Process and Focus Questions:Research says that certain principles support learning and retention. These principles will be modeled throughout both days of training. This may mean that instruction might look different than what students are used to. “Active learning practices have a more significant impact on student performance than any other variable, including student background and prior achievement.” Dr. Brigid Barron and Dr. Linda Darling-Hammond, Stanford UniversityFollowing these principles will make teaching easier.
Time: minutes (8:30-8:30)Materials: Trainer’s Process and Focus Questions:
Time: less than 1 minute (8:30-8:31)Materials: noneTrainer’s Process and Focus Questions:Now that there is sense of the overall picture of the curriculum and the goals for the course, let’s get into an actual lesson. Think about the principles that support learning and retention and the idea of rebuilding the mathematical foundation from the ground up as Lesson One is modeled for you. So for now, you will be students and have an opportunity to experience lesson one as a student.
Time: 3 minutes (8:49-8:52)Materials: Extra practice, Volume One, Lesson 1, page 1Trainer’s Process and Focus Questions:Let’s Practice. This would be a place to stop and ask students to check their homework or do one of the warm ups. It can also be a time to let students get started on their homework and/or offer individual help. Keep this time short, 2-5 minutes. Putting homework checking and/or semi-independent work time in the middle of the period optimizes learning time. Let’s students be ready to start again on the next portion of the lesson. Since this is the first day and there is no homework, we’ll do a few problems from the Extra Practice book. It will allow me to get an assessment of how well the students are understanding the material and offer individual assistance if needed. Tips:-spend less than one minute with any one student-circulate among students and look at their work. You may want to offer feedback-stamps, stars, labeling the learning, asking questions, etc.-require students to be accountable for their work (it counts!) and turn it in.-keep the time short
Time: 2 minutes (8:52-8:54)Materials: noneTrainer’s Process and Focus Questions:This is like a second Get your Brain in Gear and gets students active and engaged and ready for new learning. Breaks up the lesson into parts to capitalize on having a new beginning to the lesson.ACTIVITY: “I say review”: With partner, explain what they know about number lines. Get points for using words listed. Get extra point if use a diagram in their explanation.Give one minute for each person in the pair to talk. Model an example:We learned that the number line can be used to show expressions and equations. Expressions are shown by jumps that start at the origin, or 0, and move to a point on the number line. So this expression shows 4 + n + 6 (draws number line, labels 0 and shows jumps. Labels jumps as +4, +n, and +6). The value of the expression is shown here where the expressions ends (puts point at end of expression). It can be labeled with a variable, since the value is unknown (puts d to show value of expression).
Time: less than 1 minute (9:05-9:06)Materials: noneTrainer’s Process and Focus Questions:Now that you’ve experienced the lesson as a student, let’s look at the lesson from the teacher’s point of view. We’ll look at how engagement and questioning strategies were modeled in the lesson and how features built into the text book support the principles for learning and retention.
Time: 5 minutes (9:06-9:11)Materials: chart paper for recordingTrainer’s Process and Focus Questions:Whip around: Call out teaching strategies you experienced.-How did the lesson start?-How was your understanding developed?-How were you engaged throughout the lesson? How were you given feedback?-What kinds of questions did I ask? How were all of you responsible for responding?-Wait timeWhat opportunities were you given to explain what you knew or understood?How did you record what you learned in the lesson? How is that different from traditional note taking?What opportunities did you have to be responsible for your own learning?
Time: less than 1 minute (9:13-9:14)Materials: noneTrainer’s Process and Focus Questions:Structures in the text make incorporating principles of learning easier to implement. Let’s look in more depth at the ways the textbook supports the instructional best practices.
Time: 2 minutes (9:14-9:16)Materials: noneTrainer’s Process and Focus Questions: icon denotes feature in textbookAll teachers know the importance of actively engaging students at soon as they come in the door and that bell to bell instruction shows a positive increase in student achievement. Consider using Get Your Brain in Gear or the Remember from Before as soon as the bell rings and setting aside homework correction and a written warm up until the middle of the period. ACTIVITY: Pop Up- This come from lesson 3. What do you notice about the Get Your Brain in Gear?KEY POINTS:Prepare students for lessonReviews previously taught material needed for the lessonConnects prior learning to increase retention Affords opportunity for teacher to diagnose what may need review or reteaching, either individually or to whole class as the lesson is being taught. This is how you know what you need to modify as you teach the lessonShould take 1-3 minutes, very important that this takes no more than 3 minutes. To accomplish this, MUST have way for each student to respond to each question and for the teacher to get IMMEDIATE feedback from each student.Rule 1: Every student must be actively engagedRule 2: Teacher and students must have immediate feedbackWhat different ways can you meet both of these rules as you do Remember from Before and Get your Brain in Gear? Brainstorm in your group.
Time: 1 minute (9:16-9:17)Materials: noneTrainer’s Process and Focus Questions:Since the curriculum starts from the ground up, with the assumption that the student knows nothing and that everything will be explained and defined, it makes sense that chapter one would have lots of vocabulary. Chapter One is actually critical for developing key vocabulary. Let’s debrief for a moment about direct vocabulary instruction.Examine this chart. What does it say about how we might need to change the way we instruct vocabulary? How much practice is needed before a word is recognized automatically?Generally speaking, more exposures are needed for:Younger learnersMore abstract words Words easily confused with already known words(nouns and verbs are learned faster than function words)Gates, 1931;McCormack, l999: Montgomery,2000What ways can you help students increase their exposures to the vocabulary words?
Time: 1 minute (9:17-9:18)Materials: noneTrainer’s Process and Focus Questions:Marzano has researched components of effective vocabulary instruction. Students must represent their knowledge of words in linguistic and non-linguistic ways. How does the text support opportunities to:Represent words using graphic organizers, pictures, and graphic representations?Ask students to create mental pictures and/or act out their meaning?Use various forms of identifying similarities and differences?Compare, classify, create metaphors, create analogies?Notice there is not a reliance on definitions copied down, but instead direct instruction in both linguistic and non-linguistic ways.
Time: 3 minutes (9:21-9:24)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: What is the value in using the checks for understanding?Need to assess level of student understanding and find if and where students are stuck. Are they ready for new learning? Do they need additional practice? Have they reached a saturation point?Be sure students have met objective before moving to new section in lesson. Pushing ahead may lead to confusion.TIPS FOR USING CHECK FOR UNDERSTANDING:Use white boards or TPR (Total Physical Response, i.e. hand signals, fingers, etc. so ALL students must respond to each question) for initial problems. Allow students to write a “?” next to their guess work, if they do not know how to do a problem. Remind them we are here to learn and it is all right to NOT know how to do something. It’s not alright not to try. Asking students to put a “?” on their board gave me many benefits: I didn’t have to wait so long for all students to respond. I knew how many students didn’t really know what to do. Students felt safe not knowing how to do something, and it was less threatening than asking a question.Strive for variety. Guided group practice, scaffolding support; Small group or partner work; Mini-quiz; Independent practice Had to balance what went on the white board and what went in the notes. I found I needed to make sure that I used at least one or a part of one of the Check for Understandings as a time for students to work independently, with me checking how they were doing. Notice how we did the first problem together with lots of support and how you did the next two on your own, but with the white board so I could see how your were doing. I could have also had you work with a partner or given you a few minutes to work on it on your own while I moved around the room, checking your work.
Time: 3 minutes (9:24-9:27)Materials: noneTrainer’s Process and Focus Questions:Each lesson ends with a Check for Understanding right before the Problem Set. Each lesson has Multiple Choice Practice and Find the Errors, which are at the end of each lesson slideshow. These are wonderful ways to provide summative assessment for you and for the students. Closure is the most often skipped component in a lesson, but is very critical.The book also offers a journal question which will give you important information on what your students really understand.Use Multiple Choice Practice and Find the Errors as additional assessment.Give a short closure quiz.Begin the next lesson with a short assessment. Use this to group students according to need. Give the Math Journal Question(s) as closureACTIVITY: Share ways to use the Multiple Choice Practice and Find the Errors in your classroom.
Time: minutes (9:30-9:30)Materials: Trainer’s Process and Focus Questions:
Time: minutes (9:30-9:31)Materials: noneTrainer’s Process and Focus Questions:We’ve seen how the text starts from the beginning and rebuilds the foundation. Nothing is assumed. We’ve also seen how teaching strategies used in conjunction with the support features in the text support learning and retention. We’ve also seen how the text uses visual models to teach math concepts. Now it’s time to see that longitudinal coherence – to see how the number line is extended and applied to many different concepts and standards.
Time: minutes (9:30-9:55)Materials: Flash file, number line worksheetsTrainer’s Process and Focus Questions:Use Flash animation for the Number line.
Time: minutes (9:55-9:55)Materials: Trainer’s Process and Focus Questions:
Time: minutes (10:10-10:10)Materials: Trainer’s Process and Focus Questions:
Time: less than 1 minute (10:10-10:11)Materials: noneTrainer’s Process and Focus Questions:Begin now with a chance to get into the curriculum in depth for chapters 1 and 2. Goal is to first look at ways to specifically use the features that we have already seen and use them in planning how to present the lessons in chapters 1 and 2.
Time: less than 1 minute (10:11-10:12)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: Reflect on a time when you have taught something for the first time. It may be a lesson or a new curriculum or using a new strategy. What makes it difficult the first time? What do you learn by teaching it that makes it easier the second time? Pop up to share.KEY POINTS:Unfamiliar with the materialHaven’t found the best way to word things that help students understandDon’t know where students may have misconceptions or struggle with concepts/skillsNot sure where it is best to stop and check for understandingNot sure exactly what students are to know and understand in a lesson and how they will need to apply it.We’ll spend some time now addressing some of these issues so it will be easier to teach it that first time. As we do that we’ll also explore other features in the teacher’s edition and the student text that will help shorten the learning curve for teachers. We’ll learn how to find the Big ideas in each lesson. By learning where, how, and why students struggle, it is easier to design instruction that will help students through these difficulties.
Time: 1 minute (10:12-10:13)Materials: note paperTrainer’s Process and Focus Questions:Can be challenging to teach the prescribed curriculum and meet the academic needs of the students. ACTIVITY: Take a moment and think about the students you will be teaching. List two challenges you might experience. Now write down two goals you have for your students. The goals may or may not be relates to the challenges.
Time: less than 1 minute (10:13-10:14)Materials: noneTrainer’s Process and Focus Questions:Let’s explore how to use the resources in the curriculum along with the experience and knowledge you already have to design effective instruction. As you think about your teaching, what are the effective strategies and structures that you want to be sure to keep. List those.
Time: less than 1 minute (10:13-10:14)Materials: textbook, TE Volume OneTrainer’s Process and Focus Questions:First, let’s get an overview of what is in the program. Open books up to pages T1-T6, How to Use the Features of this Textbook.
Time: 10 minutes (10:14-10:24)Materials: textbook, TE Volume OneTrainer’s Process and Focus Questions:ACTIVITY: Read through How to Use the Features of this Textbook, pages T1-T6 in the Teacher’s edition. Highlight or use Post Its to mark important aspects you want to remember. ACTIVITY: Use “Say something” with a partner to process what was read.
Time: less than 1 minute (10:24-10:25)Materials: highlighters, Post Its, textbook: TE Volume OneTrainer’s Process and Focus Questions:Get with a partner. Decide who will initially focus on chapter one and who will focus on chapter two. Participants will need the Teacher’s Edition of Volume One and the Lesson Overview Worksheets. They may also want Post Its and/or a highlighter.
Time: 5 minutes (10:25-10:30)Materials: textbook, TE Volume OneTrainer’s Process and Focus Questions:ACTIVITY: Read the red Pacing and Resources and Universal Access pages at the beginning of the chapter you will be exploring. Share with your partner which types of support you think would be most effective with your students.
Time: 20 minutes (10:30-10:50)Materials: top portion of the Lesson Overview worksheets, textbook, TE Volume OneTrainer’s Process and Focus Questions:Turn to page 6D, Common Errors and Misconceptions for Chapter One. Model the activity with the first two misconceptions listed for lesson 1. First read the misconception, then look back in the lesson to find how that concept was addressed in the text. Then ask how the instruction, checks for understanding, questioning, and other activities that were modeled in Lesson 1 supported uncovering and addressing these misconceptions. ACTIVITY: Now work on the chapter you are exploring. Chapter One people will begin with lesson 2 and Chapter 2 people will start with lesson 6. Remind participants that they will only be filling in the chart portion of the handout.Read the misconceptions for one lesson at a time.After reading the misconceptions for a particular lesson, go into the text and skim the lesson to see which part of the lesson correlates to the misconception. Think and write how than misconception might be addressed through how the lesson is presented. Look for the Big Ideas and Key Concepts in the lesson.When finished will all four lessons, share with your partner. Tell what the misconceptions for the lessons are and how they will be addressed. Share any ideas you have about how to present the concepts to the students.
Time: less than 1 minute (10:50-10:51)Materials: noneTrainer’s Process and Focus Questions:Now that we have a sense of what a chapter looks like, let’s take a few moments to address some general pacing guidelines that will guide you in planning your instructional week.
Time: less than 1 minute (10:54-10:55)Materials: noneTrainer’s Process and Focus Questions:Now we have an idea of what the content for chapters one and two is. We’ve looked at misconceptions and how those might be addressed. We know that we need to aim for 3-4 lessons per week and that the week needs to allow for one period in the lab and any assessments that may be given. Pacing can be a challenge, especially when working with students who have struggled with learning math. There may be times when you feel there is just too much curriculum to fit in or that if you go too fast the students just won’t grasp the concepts. Finding and focusing on the key concepts in a lesson will help as you plan the lessons. We’re going to explore one way you might do that.
Time: 35 minutes (10:55-11:30)Materials: bottom portion of the Lesson Overview worksheets, textbook, TE Volume OneTrainer’s Process and Focus Questions:One way to find the key ideas is to work backwards and see what students are being asked to do. We’ll look at the end of each lesson to see what it is that students are supposed to do. As you look at what they are supposed to do, be thinking: What will students need to understand to do this work? According to what is being asked, what are the big ideas and key concepts that students will need to know? ACTIVITY: Keep the same partner, but switch roles. If you were exploring chapter one, you will now be examining chapter two. It you were exploring chapter two, you will now be working with chapter one. If you are now working on chapter one, begin with lesson 2. If you are working with chapter two, begin with lesson 6.Start by reading the Looking Back at the end of the lesson. Then do the Problem Set Sampler listed on the lesson overview worksheet (the same one they used earlier).As you are doing the problems, look back into the lesson to see how the concepts and content are presented to students. What understanding lies beneath the ability to do that problem?Think about how you might present the lesson so that students will have the understanding and confidence to do those problems.After you finish the lesson, share out what you found with your partner and record findings on the Lesson Overview worksheets.Repeat the process for the other lessons (3 with 7, 4 with 8, and 5 with 9)
Time: minutes (11:35-11:35)Materials: Trainer’s Process and Focus Questions:
Time: 3 minutes (11:35-11:38)Materials: note paperTrainer’s Process and Focus Questions:The focus and goals of the class and for the students will affect pacing issues.Who is in the class? How did they get selected?What is the goal for these students?What is the purpose of this class? How important is it to teach the pre algebra standards as compared to the foundational standards? ACTIVITY: Write down how students are selected to be in this course along with the purpose of this class. What is it you want for these students at the end of this year? How does this class fit in with the larger picture of math courses these students will take?
Time: 5 minutes (11:38-11:43)Materials: textbook, TE Volume One, note paperTrainer’s Process and Focus Questions:ACTIVITY: Look at table of contents and standards correlation at beginning of text. Some portions of book are focused on foundational standards and others are more focused on targeted pre algebra standards, though all are connected and build a mathematical foundation. Read through these pages more closely with these questions in mind:What is the scope of the Algebra Readiness course you want to offer?There is so much curriculum, that to go into all of it, in depth, is probably not realistic. Need to choose whether you want to focus on getting to and teaching the pre algebra standards or the foundational standards.What district and state assessments will you be giving? There may be a mismatch between state and local assessments and the AR curriculum standards. Will need to address how those issues will be resolved as you make your own long range plans. Will address long range plans and pacing more in depth at the second day of training. For now, decide if you want to focus on foundational standards with some pre algebra or a faster pacing through the foundational so there is adequate time devoted to the targeted pre algebra standards.
Time: 3 minutes (11:43-11:46)Materials: textbook, TE Volume OneTrainer’s Process and Focus Questions:While it is important to move through the text sequentially, not all chapters may receive equal emphasis. We recommend that all schools complete all of chapters 1, 2, and 4 to firmly establish the visual models and build an algebraic understanding of expressions, equations, and rates. These chapters are critical to assuring that the foundation for the longitudinal coherence is set. -For schools that want to focus on rebuilding the foundational standards, allow adequate time for Volumes One and Two. There may by some material in Volume Three that you want to set aside for now.-For schools that want to make sure that the targeted pre algebra standards are mastered, it will be important to allow adequate time to teach chapters 11-18 (one semester). This will mean that the foundational standards addressed in many of the lessons will need to moved through more quickly. We can work with your schools to share ways to use the diagnostic assessments to help differentiate the curriculum and give suggestions for condensing some of the lessons that focus on foundational standards that your students have already mastered.ACTIVITY: Which chapters do you want to make sure are covered before testing time? Discuss with those around you what your goals are and how far through the curriculum you want to be by testing time.
Time: 1 minute (11:46-11:47)Materials: noneTrainer’s Process and Focus Questions:There may be a mismatch between state and local assessments and the AR curriculum. Will need to address how those issues will be resolved as you make your own long range plans. (Document on right side of folder for CA schools correlating the AR standards to the CST General Mathematics test.) Will want to plan for addressing these standards. Can look at that as well during the second say of training.
Time: 8 minutes (11:47-11:55)Materials: textbook: TE Volume One, sample pacing guidesTrainer’s Process and Focus Questions:ACTIVITY: Get in groups and examine the sample long range plans. Create a draft for long range plans for your situation. We will have spend more time with your long range plans on the second day of training after you have had a chance to experience the curriculum with your students.
Time: minutes (11:55-11:55)Materials: Trainer’s Process and Focus Questions:
Time: minutes (12:55-12:55)Materials: Trainer’s Process and Focus Questions:
Time: 1minute (12:55-12:56)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: Think about what questions you have about the software component of the curriculum. Jot down your questions.Spatial Temporal Math or ST Math complements classroom instruction. Consists of a series of games that convey and develop mathematical knowledge visually, without requiring language processing.After proficiency at visual mathematics, instructs how to translate this into mathematical language.Uses animation to convey mathematical information. The animation provides immediate and illustrative feedback which shows the mathematical consequences of mistakes visually.Provides extensive practice for procedural and computational skills.
Time: less than 1 minute (12:56-12:57)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: Ask participants what the goal for ST Math is. Call on several participants. KEY POINTS:-Make all students successful in math.-Develop students as self actualized learners.-Build math competency and confidence.-Deepen mathematical understanding.ST Math will provide much for your students. But to maximize the positive outcomes of ST Math, you as teacher must have an active role in making a connection between the software and classroom instructionThe Teacher is vital to:Make connections between computer-based learning and textbook-based learningFoster mathematical communicationHelp students develop strategies and mathematical reasoning abilitiesAssist struggling students with tutoring and guidanceSUMMARIZE: In the class and in the lab, supporting students to become self-actualized learners maximizes the math learning and the ability for students to solve problems. This may look different than the way math is typically taught. Invite participants to try these ideas on and to assess the effectiveness after working with their students in these, perhaps new, ways.
Time: less than 1 minute (12:57-12:58)Materials: noneTrainer’s Process and Focus Questions:FOCUSING QUESTIONS: How can you get the most out of the time in the lab? What does it mean to develop students as self actualized learners? How do you support students who are stuck? How does teacher behavior influence student achievement? What logistics do you need to know?Want to be certain that the students learn through the games.Students will: Pair the deep understanding of the visual to the symbolic math andBuild analytical skills as they reason & translate from visual to abstract.Result: Increased student learningBring learning to a conscious level andReinforce conceptual understanding with verbal communication.Result: Increased retention
Time: 1 minute (12:58-12:59)Materials: noneTrainer’s Process and Focus Questions:Organized into same chapters 1-17 as the textbook.Beginning chapter contains timed basic facts drills.Students should be on the software the equivalent of one period per week. If there is a way for students to access the computers for additional time (a double period of math, before/after school, etc), that would be very beneficial to the students.The more the games are used, the deeper the students’ understanding. We’ll look at the structure and design of the games, analyze some games, give you a chance to play the games on your own, and see ways to use the games to connect to the classroom and the text.
Time: 1 minute (12:59-1:00)Materials: noneTrainer’s Process and Focus Questions:Each chapter contains multiple games.Each game consists of multiple levels that increase in difficulty and sophistication.Students must pass a level before proceeding to the next level.Students progress through levels and exercises in self-paced manner.Beginning chapter contains timed basic facts drills.Aligned to standards in Appendix E.
Time: 4 minutes (1:00-1:04)Materials: link to gameTrainer’s Process and Focus Questions:INTRODUCTION: The analysis process will first be modeled together, then participants will have a chance to analyze the game on their own. This will not only familiarize teachers with the process, but also give the opportunity to learn a game.ACTIVITY: Play selected puzzles from chapter 2 game: Wall Factory (Flash file)Ask participants to tell what they notice. It is the animation that gives a visual representation of the math. Looking carefully reveals lots of mathematics embedded in the game. Replay the animation a few times to allow them to elicit more responses. Focus here on describing what is happening in the animation. Use wait time both after asking the questions and after hearing the responses. Delve to get more elaboration.Looking carefully reveals lots of mathematics embedded in the game. Focus here on describing what is happening in the animation. Use wait time both after asking the questions and after hearing the responses. Delve to get more elaboration.KEY POINTS: Look for and highlight the following in the responses:What happens with both correct and incorrect selections. Observe the feedback from the animation.Describe the visualization or model presented-What concepts are being taught?-What is the visual model? How is it used to teach the concept?-What happens if an incorrect response is selected? A correct response?-How would you represent this mathematically? -What topics are covered here? -How does this relate to teaching concepts in your curriculum?-How does the visual get connected to the symbolic?
Time: 5 minutes (1:04-1:09)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: Model the process now. Show screen shot of each level, eliciting how the concept develops through the levels. Focusing questions:What is different at this level?How is the difficulty increasing?How is the amount of visualization decreasing?How is the amount of symbolic math increasing?How does the animation at the higher levels support visual understanding?How is the concept being developed?
Time: 3 minutes (1:09-1:12)Materials: noneTrainer’s Process and Focus Questions:ACTIVITY: Ask participants to examine the sequence shown in the slide, which highlights the animation that converts the symbolic back to the visual when giving the immediate and illustrative feedback.Focusing questions: What do you notice happens in each successive part of the animation? What might be the purpose of this animation? What other mathematics concepts can be taught or reinforced by slowing down and looking at each part of the animation? How might parts of the animation be represented symbolically?Possible answers: substitution, value of numbers, addition of expressions, different variables can have the same value, meaning of multiplication, multiplication as repeated addition, equivalent ways to represent the same representation.
Time: 4 minutes (1:12-1:16)Materials: computer with internet access, Teacher Console LoginTrainer’s Process and Focus Questions:Login procedure opens many resources, including game access.ACTIVITY: Login onto the website. Open up browser and type in address: www.mindresearch.net Log on to the Teacher Console.TRAINER: You may need to assist some teachers with the login procedure or ask those who are already logged in to help a neighbor. If most of participants are logged on the website, tell those who are stuck that you’ll be with them as soon as you get everyone else started on the next task. Move on to the next slide. Return to those who need assistance later.
Time: 1 minute (1:16-1:17)Materials: computer with internet access, Teacher Console LoginTrainer’s Process and Focus Questions:ACTIVITY: The access game feature used to analyze games can also be used to support students and help them make the connections to the classroom lessons. Follow the 3-step procedure to access games.Click on access gamesClick on Algebra Readiness BasalClick on chapter 8Tell participants they will have a chance now to analyze the game they already looked at together.
Time: 1 minute (1:17-1:18)Materials: computer with internet accessTrainer’s Process and Focus Questions:For this exercise, first find the Chapter 2 (marked with the arrow) and then the Wall Factory game (marked with the arrow). When on the game, begin playing level 1.
Time: 10 minutes (1:18-1:28)Materials: computer logged onto game, Game Analysis TemplateTrainer’s Process and Focus Questions:Point out graphic showing template for the game modeled on the handout. ACTIVITY: Participants may work individually or in pairs. Remind that playing the first level is a good way to see what concept or skill is being taught and how the mathematics is being visualized. Participants should play level 1, examining the animation and recording in the left column of the template.Next, play the various levels of the game, analyzing how it progresses.What happens? What happens next?Observe and record the responses to both correct and incorrect choices.What additional math concepts are being presented?What visualization or model is used?Record a synopsis of what is being asked at each level on the template. Focus on what changes from level to level.Be sure to note on which levels the question gets asked in a new way or when there are a combination of ways the problems are presented.Look for changes in amount of visualization and amount of symbols used.Look for how the difficulty increases.EARLY FINISHERS: Complete the bottom portion of the template.
Time: 3 minutes (1:28-1:31)Materials: Game Analysis TemplateTrainer’s Process and Focus Questions:ACTIVITY: Toss Around: Toss around a stuffed penguin. When someone catches the penguin, they share something they saw by analyzing the game or ask a question for someone else to answer. They then get to toss the penguin to someone else. Focusing questions:-What important math concepts are presented?-How are they modeled?-What do students need to be able to do in the game?-How might this be represented mathematically?-What do they need to be able to do in the textbook?-How might the scaffolding through the levels support teaching in the classroom?
Time: 1 minute (1:31-1:32)Materials: noneTrainer’s Process and Focus Questions:Many students are not good at making connections.In lab will see students developing deep understandings and doing sophisticated mathematics. Many won’t be able to verbalize it or write about their thinking without the support of a teacher.Facilitating in the lab is only one part of making the connection. There must be regular, consistent connections between the games and the text.Students will better understand concepts presented in the text, and increase their competence with procedures and skills.When students can verbalize what they know, they know it. AND they know they know it.The goal is for students to know the math and how we represent it symbolically. These connections are critical for that transfer to occur.The brain stores and retrieves better when there are connections and things are ‘filed’ with many key words.Easier for the students and easier for you. When students understand the math, you need only label it and show how it is represented symbolically.These are skills that will support them in all areas of school and life.
Time: 13 minutes (1:32-1:45)Materials: Connecting to the Classroom worksheetTrainer’s Process and Focus Questions:Very effective to play the games in class as a part of regular instruction. Can be done as warm up, guided practice, part of the instruction, or as check for understanding. Use to deepen understanding of the math concepts and to help see how the visualizations are connected to the math in their text.Vary the ways ST Math is used to increase motivation and/or meet the needs of a specific group of studentsTeachers MUST provide a way for each student to respond each time in a way that is visible to the teacher. If students need extra support, put them with a partner or in a team. To have students really teach one another, don’t make it competitive. Instead, reward students for explaining and talking aloud about their choices.If the students have already played the game, use it to show how to do the math in the book. Ask students to show how they solved it and then show how that can be shown mathematically so they see how to apply the same strategy to the textbook problems.If the students have a good understanding of the mathematics and can solve problems from the text, use that knowledge while playing the game. Show how the problem is written in the text right and put it next to a problem in the game. Let students see how the visual matches what they have been doing in class.ACTIVITY: With a small group, discuss how to use the game in the classroom. Discuss what steps would be taken and write them on the Connecting to the Classroom template, Using ST Math in the Classroom.Use the game as a guide to create a plan for moving from the hands-on to the symbolic. Here are some considerations based on classroom action research:-Ask students to draw a diagram to represent the visual model. -Ask students to write the symbolic alongside the visual.-Ask students to visualize the action required without making the action with the materials.-Ask students to look at the symbolic and visualize the model.-As needed, ask students to move back to the visual to check work.When finished, may use any extra time to explore other games from chapters 1-3.
Time: minutes (1:45-1:45)Materials: Trainer’s Process and Focus Questions:
Time:Materials: Trainer’s Process and Focus Questions:
Time: 3 minutesMaterials: Trainer’s Process and Focus Questions:Go over each part of the report. Key Points:Review before each time students go to the lab.Explain current chapter and current gameExplain tries and extra playsAim for 50% or more of each chapter complete if possible
Time: less than 1 minute (2:00-2:00)Materials: Trainer’s Process and Focus Questions:
Time: 3 minutes (2:00-2:03)Materials: Facilitating in the Computer LabTrainer’s Process and Focus Questions:Read page Facilitating in the Computer Lab, highlighting four important ideas. Use ‘Say something’ to process. SUMMARIZE:Students play the games independently to build spatial-temporal reasoning ability.Teachers use questions to facilitate learning movement when students get stuck.Teachers label the learning and the mathematics for the ST Math games.Teachers make explicit connections between the ST Math games and the symbolic mathematics processes.Teachers design opportunities that require students’ mathematical communication.Instead of telling student the answer, ask guided questions that will lead them to find the answer on their own. Important to show these students they can learn. They feel empowered by their success in figuring things out for themselves.Important to see how everyone is progressing. When see red bar covering 80% or more repeatedly, it is time to step in.It is essential to not provide answers. This enables the student to move on before they’ve mastered a concept.Don’t tell how a game works or what they need to do. Question students, ask them to explain the animation. Page of facilitating questions here. (have participants pull this page from their folder)This is not a time for student tutors. They give too much assistance and the student won’t grasp the concept on their own.This journal is for you. It will help you in making the connections, learning how the math is presented, and give you opportunities to see how the visualizations from the games can be used to support your classroom teaching.
Time: 3 minutes (2:37-2:40)Materials: note paperTrainer’s Process and Focus Questions:ACTIVITY: Set rules for the lab. With a partner, discuss no more than three rules for student behavior in the lab. Record the rules in the box at the bottom of the page.ACTIVITY: Share what supplies other teachers have found helpful to either bring to the lab or keep in the lab. -student roster-scratch paper-pencils-place to write down notes about students or about the games-Teacher’s Manual or Scope and SequenceParticipants write down the items they wish to bring in the toolkit and where the toolkit will be kept.
Time: minutes (2:40-2:40)Materials: Trainer’s Process and Focus Questions:
Time: minutes (2:46-2:46)Materials: Trainer’s Process and Focus Questions:
Time: 2 minutes (2:46-2:48)Materials: Computer logged onto Teacher ConsoleTrainer’s Process and Focus Questions:ACTIVITY: Let’s learn how to update your profile.First find the Update Your Profile box in the upper right hand corner of the screen. Click on the box.Second, please check the email address shown. If it is correct, you don’t need to do anything. If it is incorrect, please click Update Info. If you wish to change your password, you may do so. The number of stars is always 16 as a security measure.
Time: less than 1 minuteMaterials:Trainer’s Process and Focus Questions:Team of support for you as you implement the curriculum
Time: minutes (8:17-8:22)Materials: Trainer’s Process and Focus Questions:
2 Day Training Day 1
What does a MIND Algebra Readiness class look and sound like?<br />What do I need to do to connect my students’<br />visual learning in the games with their <br />abstract symbolic learning of mathematics?<br />ST Math: what is it? How do students use it?<br />What is the Algebra Readiness course? <br />What mathematics is taught using the number line?<br />How does the MIND Algebra Readiness course support me to guide ALL my students to mastery?<br />What’s so different about this curriculum that students who have never been able to do math before suddenly get it?!<br />What are the components of each lesson and how is each significant to student learning?<br />What resources are provided?<br />How do I facilitate learning with ST Math?<br />
The MIND Algebra Readiness approach supports learning.<br /><br />Students rebuild a mathematical foundation.<br />Structures support learning and retention.<br />Visual models and teaching Big Ideas provide longitudinal coherence.<br />
5AF 1.0<br />Use variables in expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.<br />Chapter 1Lesson 1<br />Your First Trip to the Number Line<br />
Objectives<br />Use variables in simple expressions and equations.<br />Represent expressions and equations on the number line.<br />
Get Your Brain in Gear<br /> 1. Count from 0 to 10 as fast as you can.<br /> 2. Count by 10’s from 0 to 100 as fast as you can.<br />
The number line is a perfectly straight line that goes on forever in both directions. <br />Question: What percent of all lines are perfectly straight?<br />We can draw only a small part of it here:<br />The arrows ( ) drawn at the ends mean the line continues on and on forever.<br />Answer: 100%! All lines are perfectly straight.<br />
Normal things in the world have thickness, buta number line has no thickness.<br />
The number line is made up of infinitely many points.<br />Each unique point represents a unique number.<br />To show a number on the number line it will be marked with a or a .<br />
If you pick any two points on the number line, there are always infinitely many points in between them.<br />No two points touch each other.<br />
There are two important points on the number line that we will use to define where all the other points are located.<br />These important points are the numbers 0 and 1.<br />Partner Talk:<br />A– Explain to B why you think the number 0 is important.<br />B– Tell A why you think where the number 1 is put is important.<br />
The zero point is sometimes called the origin.<br />Zero separates the number line into positive and negative sides.<br />Zero is neither positive or negative.<br />Going to the left takes you in the negative (-) direction. These numbers to the left of zero are called negative numbers.<br />Going to the right takes you in the positive (+) direction. These numbers to the right of zero are called positive numbers.<br />
Check for Understanding<br />1.Which of the following points are positive? Which are negative? Explain your reasoning. <br />Points _______ are positive because ____________.<br />Points _______ are negative because ____________.<br />Check for Understanding 1<br />
The point zero is called the origin because we always start at zero to get to any other point. In this book we will move along the number line using jumps.<br />Origin means “the place where something begins”.<br />A jump is indicated by a curved arrow. Here is a jump that takes us from zero to one.<br />The distance traveled is shown above the jump.<br />
Jumps can also be shown below the number line.<br />The distance of +1 is called a whole.<br />A whole is the distance from 0 to 1 on the number line.<br />
The following jump has a distance of more than a whole. <br />A: Tell B how you know it’s distance is more than a whole.<br />B: Tell A what “a distance of nmeans.”<br />What do we mean by a distance of n?<br />In math, we use letters to represent unknown values.<br />These letters are called variables. We can treat a variable as a number.<br />
Check for Understanding<br />2. Identify the distance traveled by each jump and indicate if it is more or less than a whole:<br />Write a sentence in your notes that explains how you know if a jump is more or less than a whole. Trade your notes with your partner and make certain you both agree.<br />
We define addition as placing the start of a jump at the end of an existing jump.<br />This shows 1.<br />This shows 1 + n.<br />The + sign represents addition because we are adding +1 and +ntogether.<br />1 + nis an expression. An expression represents a path from zero to a point on the number line.<br />
Check for Understanding<br />3. Use symbols to write the following expressions:<br />
An expression tells us how to get to a point on the number line. That point is called the value of the expression.<br />This expression has a value of 6 .<br />We can write the expression as 1 + 1 + m.<br />The value is 6 because the final jump lands on 6.<br />What’s the difference between an expression and the value of the expression?<br />
Check for Understanding<br />4. Use symbols to write the following expressions. What is the value of each expression?<br />
Let’s Practice!<br />Extra practice Page 1<br />#1-12<br />
How many points can you get?<br />“I say” review: <br />Tell your partner something you have learned. <br />Your partner will give 1 point for each word you use and explain.<br />Get an extra point for using a diagram to help explain.<br />Number line Positive<br />Negative Origin<br />Expression Whole<br />Variable Value of an expression<br />
Adding two expressions means placing the start of one expression at the end of another expression.<br />When added together, we get a new expression. <br />Consider the following two expressions:<br />How is each expression written using symbols?<br />How is this new expression written?<br />
Check for Understanding<br />5. Use symbols to write the addition of the following two expressions:<br />Check with your partner: did you write the same sum? If not, are you both right? Why or why not?<br />Check for Understanding 5<br />Check for Understanding 6<br />
When two expressions arrive at the same point on the number line, we say that the expressions are equal.<br />By stating that two expressions are equal, we form an equation.<br />How would this equation be written?<br />An equationstates that two expressions lead to the same point on the number line.<br />
Check for Understanding<br />6. Use symbols to write the following equations:<br />
Multiple Choice Practice<br />1. A letter that is used to represent a number is called: <br />the origin<br />a variable<br />a whole<br />an equation<br />
Check that you know before you go:<br />How do you show an expression on the number line? (Try n + 2) <br />How is an equationrepresented on the number line? (Try h+ 3 = 5)<br />How is the value of an expression representedon the number line?<br />Write an expression and an equation. Label each to show you know the difference.<br />HOMEWORK<br />Page 13, # 1, 3, 5<br />Page 14, #6-14 even<br />Page 15, #18-24 even<br />
The MIND Algebra Readiness approach supports learning.<br /><br />Students rebuild a mathematical foundation.<br /><br />Structures support learning and retention.<br />Visual models and teaching Big Ideas provide longitudinal coherence.<br />
Teaching strategies build students’ confidence and competence.<br />
Monitor and Adjust <br />Check for Understanding<br />4. Use symbols to write the following expressions. What is the value of each expression?<br />
Features in the text support learning and retention.<br />
1. Quickly find the value of each expression when h = 7.<br />a. 3 + h<br />b. h + h<br />c. 5 + h<br />d. 8 + h<br />2. Quickly find the value of each expression when w = 9.<br />a. w + w<br />b. 7 + w<br />c. 3 + w<br />d. 8 + w<br />
Research Says: Factors in Language Recognition<br />Exposures<br />Cognitive LevelIQ Range Needed<br />Significantly Above Average 120-129 20<br />Above Average 110-119 30<br />Average 90-109 35<br />Slow Learner 80-89 40<br />Mild Disability 70-79 45<br />Moderate Disability 60-69 55<br />Gates, 1931;McCormack, l999: Montgomery,2000<br />
Students must represent words in linguistic and non-linguistic ways.<br />
Definition<br />Non-Linguistic<br />A path from 0 to a point on the number line<br />Frayer Model<br />Expression<br />2 + h = 8<br />k + h<br />v + h = v + h <br />3m - 5<br />17<br />n = 3<br />Examples<br />Non-Examples<br />
The MIND Algebra Readiness approach supports learning.<br /><br />Students rebuild a mathematical foundation.<br /><br />Structures support learning and retention.<br /><br />Visual models and teaching Big Ideas provide longitudinal coherence.<br />
Use features of the text to support instructional design.<br />
Plan instruction that addresses key components in the lesson.<br />
Balancing student needs and content demands challenges. <br />
Use the curriculum to design effective instruction.<br />
Plan instruction forChapter One and Chapter Two.<br /><br />What is in the program?<br />What are the Big Ideas?<br />What does a week look like?<br />What is the focus in each lesson?<br />
Get an overview of the curriculum.<br />Teacher’s Edition<br />pages T1-T6<br />
Plan instruction forChapter One and Chapter Two.<br /><br />What is in the program?<br /><br />What are the Big Ideas?<br />What does a week look like?<br />What is the focus in each lesson?<br />
Use chapter resources to find the big ideas and key concepts.<br />Chapter One<br />Pages 6A, 6B, 6C<br />Chapter Two<br />Pages 54A, 54B<br />
Use chapter resources to find the big ideas and key concepts.<br />
Plan instruction forChapter One and Chapter Two.<br /><br />What is in the program?<br /><br />What are the Big Ideas?<br /><br />What does a week look like?<br />What is the focus in each lesson?<br />
Plan instruction forChapter One and Chapter Two.<br /><br />What is in the program?<br /><br />What are the Big Ideas?<br /><br />What does a week look like?<br /><br />What is the focus in each lesson?<br />
Target instruction onkey concepts and big ideas.<br />Objectives<br /><ul><li>Evaluate expressions for specific values of a variable.
Find solutions to equations with two variables.</li></ul>Problem Set Sampler: please do numbers 6, 8, 9, 11, 13, 17, 21, 22, 26, 29<br />What are the Key Points and Big Ideas students need to know from this lesson?<br />
Design the course to meet district/school/student needs.<br />What are the goals for these students?<br />Who is in this class?<br />How did they get selected?<br />How important is it to teach the targeted pre algebra standards as compared to the foundational standards?<br />
Provide curriculum that targets the goals of the course.<br />
What will you select and how will you pace to meet your goals?<br />
Practice by accessing games, 4-5 version<br />Algebra Readiness<br />Chapter 2: Describing Situations<br />Game: Wall Factory<br />1<br />2<br />
Record the progression through the levels of the game.<br />
Connect the visualizations to important math concepts.<br />
Create connections; bring the games to classroom.<br />?<br />
Make the Connection from<br /> classroom mathematicsSTMath <br />Using ST Math in the Classroom<br />Principles that support learning and retention:<br />.Students build their understanding.<br />.Students practice with feedback.<br />.Students verbalize their understanding.<br />.Students review frequently and over time.<br />Chapter: _2 Describing Situations____ Game: __Wall Factory__________ Level: ____<br />Math Concept(s):<br />Visualization:<br />What will the problem in this game look like in a text or on a test?<br />What ways can I use this game in class? How will students practice with feedback? How will students transition from the hands-on to the symbolic? <br />Facilitating questions and activities that ask students to verbalize their understanding.<br />Opportunities for frequent practice over time.<br />
Return to the homepage of your teacher console.<br />1<br />Click Add Students(AR)<br />to add your class.<br />2<br />
Check to make sure your class information is correct.<br />3<br />Make sure you’ve selected the correct Group to add your class to.<br />4<br />6<br />Click Continue.<br />Carefully enter your students’ last name, first name, and Student ID. Use their school id as their student id. This is a unique number that the students already know. For example, enter: Theresa, Jones, 1143293<br />5<br />
Review your students’ names and IDsto make sure that the information is entered correctly.<br />7<br />Click Edit if you want to make corrections to the information.<br />8<br />If the information is correct, click Add Student(s) to continue.<br />9<br />
The SCD is the students’ ST Math code. They will need this code to log into their account.<br />10<br />The Student ID is the students’ password. They will need this to log into their account.<br />11<br />Click Print, to print your class roster. This is the only time your students’ full name will appear on the class roster.<br />12<br />
Return to the homepage of your teacher console.<br />1<br />2<br />Click Teacher <br />Forum.<br />
Online forum made available to all teachers in the program.<br />Discussions.<br />Post questions.<br />To add a new topic to the list, click Start a new discussion at the top left corner.<br />
Students Access Games<br />At<br />School!<br />
Double-click the ST Math icon on the desktop of your school’s computer.<br />Give the software a moment to launch.<br />1<br />School Computer Desktop (PC or Mac)<br />
Have the student enter his/her user name and password. <br />2<br />The user name is their student code (SCD) and can be found on your class roster.<br />STE001<br />1150239<br />The password is the student id or school id.<br />Click the check mark.<br />3<br />
All the modules (chapters) are open for the students.<br />Click on the module/chapter to access the games for the chapter. <br />4<br />
Student’s code<br />Students only have access to the first game in the module. He/she must pass the game before he/she can move on to the next one.<br />Click on the game. <br />5<br />
Students only have access to the first level in the game. He/she must pass the level before he/she can move on to the next one.<br />Click on the level. <br />6<br />
Data was sent to the MIND Research Institute’s server “behind the scenes” and ST Math will close.<br />Note: Student data is also stored locally on the computer they are using. <br />
Successful Data Transfer<br />Data is attempting to send. Allow the computer time to send the data.<br />Data has successfully sent to the MIND Research Institute server.<br />The next time students log in their progress will resume from where they left off.<br />
Unsuccessful Data Transfer<br />Data is attempting to send. Allow the computer time to send the data.<br />ST Math was unable to transmit data to the MIND Research Institute’s server at the moment.<br />ST Math will send the data at another time.<br />If this happens repeatedly on a computer, check your internet connection.<br />