Yolanda DeLa Cruz

YOLANDA DE LA CRUZ:

OK. I’m Yolanda De La Cruz.  I’m an associate professor at Arizona State University West.  A Professor of Mathematics Education, uh, my name is Yolanda De La Cruz.

OK.  Uh, the---my spir---spiral model for improving mathematics, uh, is a very complex and abit---ambitious model.  What it’s doing is, it’s showing spiraling changes that happen with the teacher.  Spiraling what happens with parents and spiraling what happens with the students, and they’re all interlinked.  And what it’s doing, it’s showing the growth, when they work together, uh, when certain things happen, that they’re all happening and each one is affecting the other.  So it’s like a three dimensional model.  Uh, right now, uh, what I present, uh, what I’m working on is the final version.  I have the teacher and, uh, the parent spiral part of it now I’m working on the student part, spiral.  Because, it’s---once that link, that connection happens, then many thin---many changes happen within the, uh, the---with the parents and the students and the teachers.

I think they’ll see that there’s no---

OK, but we’ll call it the spiral model.

When---when---when people use the spiral model, what it will do is, it will show them that growth can happen.  That teachers can make changes.  That parents can make changes.  They can improve in mathematics and that it’s not happening the same time in the same level.  Uh, one teacher might be trying this, there is no, uh, particular formula that’s going to get that, it’s---it’s, uh, it’s, uh, it’s---it’s steps, it’s, uh, foundational changes in the teaching, foundational changes in the belief and foundational changes about self with the child, what they can do.  And it’s showing that they’re happening with---within, um, within a range, I mean it’s like my first step.  They’re happening, uh, maybe in different levels.  And for every student it’s going to be different, for every teacher it’s going to be different, for every family.  And it just shows that---that---that the complexity of it, but that it all works together, but then there’s room for all the individual differences within teaching style, parenting style, student-learning style.  And it just tries to capture the complexity of what happens, but that---my model is trying to capture that it can happen.  But it’s showing the inner correlations with the changes that are taking and why.  For example, the first step in a teacher, uh, would be: seeing the need for change.  We’ve---we’re getting a lot of Latino students in the schools. We’re getting a lot of diverse students.  Teachers aren’t---teachers haven’t been trained or educated in working with that diversity.  And a lot of teachers try, for a while, um, models that they learned in the university that are now outdated. Um, and unfortunately our universities aren’t---offering the classes fast enough to affect the present population that we have in the schools.  So what we’re seeing---is that we’ve got the changing student population and teachers that have no idea how to work with the diversity, uh, in the students.  And if you---if they’re schooled in the old literature that talks about minority deficit parents, they don’t care, then they’re going to believe that for a while, until something happens, whatever that something is.  That something, and some of my teachers have been---they’re good teachers, but they no longer can work with, uh, say, uh, Spanish-speaking students because they don’t speak the language.  So, they start, uh, using our reformed curriculum, uh, from Children’s Math World, uh, that’s funded by the National Science Foundation.  And they start using our reformed curricula, like the one that we have created, uh, and they start seeing that there’s many entry levels that students can learn.  Uh, for example, they start using more visuals.  Uh, they find out that just, uh, uh, repeating instructions in a different way, or having another student repeat it to another child, they’re finding different methods that can change the outcomes of a student.  And then they start seeing these little changes that they’re making, uh, they’re seeing it reflect in the grades, in the child feeling more comfortable about themselves.  Teachers start seeing these children as a different kind of students, as learners, capable learners.  Uh, they start wanting more.  So then the second step of that would be, they’re reaching out to the parents.  They’re ready to reach out for parents.  Uh, they can’t speak the language so they start, um---our curriculum has---our children’s math world curriculum has, um---it’s written in---in English and in Spanish.  Teachers start sending this material home.  Uh, they don’t need to speak it, they just start stapling the Spanish, uh, uh, page with it.  Sending it home.  They start seeing it come back.  Um, that’s---that’s uh, uh, a subtle way of communicating to parents that, yes, we’re taking your difference into consideration, but we’re trying to work with you.  You start seeing parents as trying to approach teachers, uh, in a---in ways that weren’t done before.  You’re starting to see, uh, teachers demanding bilingual office personnel, bilingual people in the classroom, people to help them with these families, to kind of like make that connection more solid.  And um, the spiral models tries to talk about this complexity but seeing that it is possible.  It’s so slow in the beginning to get started, but it can---it can happen, and it----a teacher doesn’t have to change, uh, in---in a way that they---they don’t have to become bilingual, fluent bilingual.  They can just change some of the things that they’re doing, or kind of be more sensitive to---to certain things that they---that, uh---for example, making sure that things get understo---stood.  Asking questions.  Allowing the students to ask questions if they don’t understand.  Uh, allow for sharing to happen in the classroom so that when a lot of these, uh, things start happening in the classroom we start seeing, uh, more of these needs being addressed.  But then it has to start from the teachers.  The teacher has to want this kind of change.  One of the things that we’ve found is if it’s administrative, forced on teachers, teachers are going to resent it.  They’re not going to want to try it.  And one of the things that we’ve seen, and we’ve worked with enough teachers, we’ve worked with over 250 teachers, and we’ve found that they have to take the first steps.  They have to want to change.  You can’t force a teacher to change if they’re not ready.  They have to come to that, or something---something they’ve read, articles, or whatever, saying, ‘well, I can do this.’  And once they see that this is doable, then they start trying to create those changes in the classroom.  One of the things that we’re doing now is, we’re creating, uh, um, DVDs.  And what the DVDs do, and---and our web site also has that, our Children’s Math World web site, you can tap into that and seeing some of these, uh, strategies happening in natural classrooms.  Teachers see this happening in a classroom and they’re going to say, ‘I can do that, that’s doable.  I want to try this in my classroom.’  And then the next thing is, they can, uh, they can either request it, they can reath---request our, um---uh, videos on how to have these, uh, happen in the class.  For example, we have a video that we’ve put together.  It’s uh---it’s uh---uh---a home-helper video.  And it gives them the---it outlines steps, broad, foundational steps that they could use to---to outreach, uh, more effectively to parents.   Because the outreach, or the intervention, that was in the past was for a general, monolingual type of family.  We don’t have that, uh, any more as the norm.  Now the norm is, we’ve got the diversity in many different levels, um, be it low income, uh, uh, low income students.  Students the, uh---that don’t have access to certain learning, single-family parents.  It’s just---it’s not just a---a matter of, uh, uh, Spanish-English, it’s---it’s a whole range of things that are happening now.  Um, single parents raising children, and we---we need to make these strategies, these things that are going to work, more accessible to them.  And one of the things that we’re trying to do is, um, we have our web site they can tap into.  We’re also going to create CD ROMs, or---sorry, DVDs that can be put into the computer that anybody could see, uh, say, this lesson being taught and---and kind of get ideas of---of, you know, what it’s going to take to be able to get this kind of classroom.  And again, it’s not a process that happens overnight.  It’s going to take a while to change the way that teachers think and see these children.  But, from what I’ve seen, it just takes a few times for teachers to see what these simple little changes can produce within their students, and the help that they can get parents.  To come in and---and---they don’t have to physically be there, they can help in other ways.  For example:  in our curriculum, in our Children’s Math World curriculum, we have, um, parent booklets that parents could, uh---parent booklets that---that teach parents how to help in the home.  For example: one of the main things it’s saying, find a homework helper.  Maybe you work at night.  Maybe it---maybe you can’t help you child after school but just identify a homework helper so that child can go to that person and say, ‘I need help with this.’  So that it doesn’t have to be the parent that’s doing this, it can be, uh, a neighbor, uh, a---extended family member, older sibling, a cousin, somebody that’s available to help this child when they need help.  So that child knows, if I get stuck I know that I have some access to somebody that can help me.  Uh, that’s the first one.  Another, uh, um, major change that is made by our teachers is that they can see that they’re starting to get more information on the personal, complex lives of the students.  And it’s starting to change the stereotype that these parents don’t care.  They’re seeing that these parents are overworked parents with very busy schedules, some of them holding two or three jobs, that can’t take the time off to make these, uh, teacher, uh, uh, conferences during the time of the day, uh, when---when---when they’re, you know, when they usually schedule them.  Uh, one of the things that we’ve found effective is, sometimes teachers meet on Saturdays.  Uh, sometimes they, uh, they offer these uh, uh, meetings with parents late in the afternoon or in the evening and it doesn’t take a lot of times for parent---teachers to do this so that parents start having a deeper appreciation for what the teachers giving up to be able to meet with them.  And one of the things that we’ve seen, um, when---we also offer, uh, we also do math night trainings so that teachers, uh---the math night training, what it does, is it, um, it---it brings parents, teachers and children together so they can learn about the math that’s being taught in the classroom.  So it’s going to be---have immediate, uh, feedback into what the child---to help the child in the classroom with---with the concepts that they’re learning at the present time.  And, uh, one of the things that we’ve seen is, parents will go to great efforts to be there when they know that this is going to be cost effective in their student’s learning.  Another thing that we’ve done in the University is, that, every year we get funds from somewhere and we bring, uh, four classrooms to the University for a morning, with the parents.  We take these students that have never been to the University before, parents have never stepped inside of a university classroom, and we have a math workshop for the students with the parents.  And we’ve had, uh, newspapers write us up, we’ve had the radio, we’ve been on TV before, we do this every year.  And every year it’s such a big scandal because this is so innovative, but it’s really simple to do because it holds universities accountable for this kind of learning that needs to be happening, not just in the schools, but make the universities accountable for this practice type of thing.  Um, so what we do is, we bring the teachers, um, with---the---bring the students with the parents.  Once they get to the University, we have like an introduction.  We bring students that look like students, university students, university professors, that look like these children, and talk to them.  And say, ‘yes, I, you know, I’ve done this and I come from this kind of background.’  They tell their stories, how many---how hard it’s been, but that---that it’s worth it.  You’ve got to stick it out because high school’s not going to be enough any more.  So we’ve got role models that look like them telling them, ‘this is here for you, this was here for me.’  Um, and then we take them a tour.  Uh, we---we usually take them a tour around campus, with the parents, and when these kids come back, when they leave at 1:30, you go and ask them, uh, what they’re going to be doing and they---they’ll---the majority will tell you, ‘I’m going to come to this university when I’m older.’  And it---what it does is, we’ve interviewed teachers and parents, and what it does for teachers is, they start seeing these students in a different light.  They’re starting to say, uh, they’ve told me that, ‘I never looked at this child as future university material.  Now when I see Rauel, Ramon, uh, Isabel, I see them different now.  I see that my job is to get them ready to go to Universities.’  And parents now know that high school is here, that’s---that’s the beginning step.  They’re---they are now seeing their kids with---with, uh, more roads to travel and they’re---parents are kind of equipping themselves as well, to prepare for this.  Uh, and then another thing that came out of this is that, um, uh, to see all these minority students, in a university, was scary at first for the faculty, the personnel at the university.  When the students would go through the library, so well behaved, everybody always remarked, ‘wow, those students were so well behaved.’  So they’re kind of changing the culture of the university, the way they look at these students, uh, that, you know, they might, you know, to them they were---they looked like these gang members they see on TV or they read about.  And these---these children are thanking them, being polite and they’re seeing them in a different light.  So in a way we’re kind of educating everybody.  And in the beginning I had a lot of opposition, uh, toward that because they weren’t sure if this was going to work.  And now this is like, um, I’ve got other faculty members now helping me organize these field trips to the university because they’re seeing how critical they are in changing this---this, uh, this deficit culture that---that we see, that we have, this deficit feeling that we have toward, uh, diverse students.  So that’s one of the things that the spiral model is trying to capture.

OK.  What---what we need, uh, to have good mathematics teachers for our bilingual students is, we need to have a commitment.  We need to have an honest, sincere commitment.  Not just from teachers, but from administrators that are going to support these practices.  Usually, what we’ve found, it’s been teachers forcing administrators to---to pay for the bus fare to the university, for example.  But once they get letters back, uh, uh, um, they get the information back from the university, how well behaved these students were, uh, from the parents raving about it, then it forces them to allot this money for the bus trip.  So it’s kind of been teachers having to fight for these things and unfortunately that’s how it is every year.  Um, and one of the things that I’m seeing that, um, it---it’s---it’s going to have to come from the parents, right now, asking for it, because I think the administrators are so busy doing what they’re doing that they’re not seeing that these simple practices can make a big difference, that they’re very cost effective.  Um, and also, we need, uh, a lot of inserviceing because teachers are teaching in a real, say, out-model way of mathematics that is teaching students just wrote learning.  We need students that are thinkers.  We need students that can think, uh, critical thinkers.  And when you’re just expecting wrote learning, that’s just the first step.  That’s just teaching a child to memorize, to parrot.  What we want with the---the way technology is going, we want thinkers, we want thinkers that can, uh, figure out programs, uh, have jobs that---that aren’t ev---right now they’re not even created.  We don’t even know what kind of jobs these students are going to have in the future.  We’ve got to get them ready to be thinkers and to be able to figure these things out.  And if we keep the programs that we have now where we have this wrote learning, uh, teachers afraid to try this because they’re going to get, uh, disruptive classrooms.  Then we’re---we’re con---we’re dooming these s---students to failure.

I think they need to start getting some of the terials---materials that they have, having some of them translated.  Because, uh, students become surface bilinguals but that doesn’t mean they have the language of the educational, what we call, um, educational literacy, they don’t have that yet.  And they’re learning, uh, they’re learning concepts in another language that isn’t connecting to what they have and if we help them with that link, to have things in their, uh, first language, then it’s going to, uh, um, the possibility of them understanding this is going to be so much, um---it’s going to make a difference because they’re going to be able to connect with that in some way.  And it’s just kind of giving them that little bit of extra step that they’re going to---that they’re going to learn.  It’s already hard learning mathematics, um, with---with the---with the new concepts.  Uh, it’s already hard to learn mathematics; the---the difficulty level gets harder in the junior high.  And if you have some kind of help with the language then that’s going to ensure that the internationalist---ism of mathematics is going to make that connection.  By having the child get this information in their first language.

Make sure that---that when they, um, grouping is one of the---the things that the students da---do, is---the teachers do, is they can put, say, three or four together and make sure one of them is a broker that can either translate or rephrase what the teacher said to kind of help this student, uh, understand better.  So the grouping’s important.  Another thing that is important is the---the family education.  Uh, families need to be brought into the school.  Um, I just, uh, uh, interviewed a bunch of parents, uh, for a project and one of the things that the parents are saying is, ‘we’re intimidated by the school.  You know, we feel like we don’t belong there.’  Make us feel intimidated or---dar---uh, or make us feel, um---make us feel like---like--- (self interruption)

Don’t make us so intimidated; make us feel like this is part of our community as well.  And one of the things that, uh, parents are saying is, the teachers don’t---they understand that teachers don’t do this intentionally, but that’s the message that the teachers, uh, give out.  I think part of that---part of this is because teachers are so busy they don’t realize what a first confrontation or first meeting with parents, or students, that---that---if---if—teacher’s so busy that she’s not able to take time out to pause and---and just say something to---to make a con---a personal connection with that student, that’s going to stick in that student’s mind for months, maybe the whole year.  And if the teacher makes a conscience, uh, way of trying to connect with these students in the beginning, even if there’s language barriers or whatever, that child is going to feel connected to that teacher.  Like, this teacher’s here for me.  And I think that’s really important, that’s---that’s something that, uh, you don’t need to get any of this stuff translated right away, but that is critical, that first meeting, so that the students feel welcome.  Parents feel welcome.  And once that’s set then the child’s going to feel like, ‘I have an advocate here that’s going to work with me or that I can go to them.’  And I think teachers need to be---made aware of how critical that---that first meeting, that first, uh, um, time that they’re together, that’s it’s a positive one, to make that a positive meeting.

What steps should a school take to make more connections?  Um, I think one of the things is, um---don’t wait for, um, to make connections with parents when they’re negative things.  Like when the student’s doing something wrong.  Uh, use something positive that the child’s done and write a note home or make a call home so that parents aren’t seeing a teachers as always a source of something negative that their child has done, but make them, um, somebody that---that---that’s re---acknowledging their child and saying, ‘look, we’re here to work together with you, with your child.’

Well, one of the things that---that I, uh, saw in the beginning of, um, my research studies, in working with teachers, is you saw a lot of this culture of negativism.  And, uh, the cultured negativism its---well---like in Arizona, I mean, there’s never enough funding.  There’s never enough support.  There’s---there’s a lot of things that we cannot change.  Um, and---and part of it is---helping teachers realize that no, we---we can’t change that.  We can’t make these students, uh, overnight, become English speakers.  Let’s try to see them more as like our children and see them in that light.  And then let’s see how---how much harder we’re going to work to try to make ‘our’ children successful in our schools today.  And once teachers start seeing these stu---students as their children, I mean, their children completely, then that’s when these changes start---start happening.  But it---it’s---as long as a children is---the children are aliens to them, the terms that we use in the news, uh, uh, we---we---we call our immigrants aliens and we---we give them these names like they’re---like they’re something from another planet.  As long as these students are seen like that, uh, then---then that change is not going to happen. And, um---I don’t---I don’t know how that---I---I’m still struggling with how to change that so that our students aren’t looking---aren’t looked at as aliens.   And part of the things is, um, let’s change our teachers that talked about our children as aliens is just bringing up the language of how the media portrays these students and how much of it we kind of soak in and just, uh, uh, without realizing that’s how we view them.  Uh, part of that’s---part of what’s helped break these bridges down is seeing these students as real human beings by finding out, just asking them about your home life and---and being more connected to what their realities are.  Um, because I know now, I---in fact I just went to a talk where, um, they’re saying that 85% in some states are children of minority students.  Ninety-five percent are Anglo teachers, so there’s a big cultural gap there.  And it doesn’t have to be a negative cultural ha---uh, it doesn’t have to be a negative thing.  I’s talking to a professor last night---or, I’m sorry, I was talking to a teacher last night.  Teacher said, ‘these students come here and they see me as an Anglo teacher,’ she said, ‘but it takes just a couple of weeks for them to forget that I’m Anglo and realize that I’m there for them.  And I’d---I---the first two weeks I really make it, uh, a point to make sure that I’m creating the kind of atmosphere where these students see that this classroom environment, this is our home.  This is ours.’  And whatever teachers can do to make that their classroom, that the---to be---to create this kind of environment that’s going to make it theirs then that bonding’s going to happen.  Whether teachers realize it or not it’s going to happen because there’s st---going to---as well, start seeing these students in a different light and seeing beyond their differences.

I think what---what schools should---what information they could give---sh---should give to parents in the beginning is to let them know that they’re welcome.  Let them know that---that beyond these doors, you’re---you’re welcome beyond these doors.  Um, asking for volunteerism even if parents don’t go or can’t go, just parents knowing that ‘I can come to the school.’  Uh, letting them know that teachers are available.  That---that people, uh, administrative personnel, is available.  In other words, open those doors so that is goes both ways so parents can feel comfortable in coming in.  Um, I’ve seen that done by having, uh, uh, pot lucks in schools, just to create this kind of atmosphere.  And I’ve seen the successful schools are the ones that make parents feel like, ‘this is my community.’  This is---this is mine as well.

 Oh, uh, Alice comes to mind.  Alice start working with us five years ago.  She wanted, uh, to learn, uh, this, uh, uh---reform mathematics.  She wanted to incorporate the standards, the State and National standards in the classroom and she became part of our research project, because she wanted to pilot our Children’s Math World curriculum.  And I remember her---s---kept on talking about, ‘those children,’ uh, are so hard to teach.  And ‘those children’ are, um, not learning these concepts.  And the parents, um, the parents aren’t, uh, coming in when I ask them to come in.  And one of the things that I see myself is, I’ve lived long enough in this life so that I’m tolerant of these things, um, I---I no longer get angry or react to them.  I’m just at an age, now, where it’s like, well, what can I do to kind of like---help this teacher make connections?  I have to be a mentor to all students and I have to see students at their---they have to become mentors for all students as well.  So one of the things is, um, ---making literature available.  Um, myself, or part of my t---my team going and actually working with a teacher in the classroom, uh, with either DVDs or videos.  Um, helping them experience success with using these first, uh, step methods I talked about, which are, um, trying to---bridge home communications.  Trying to get her to see---to know her students better.  Trying to use more visuals, uh, when they’re, uh, teaching mathematics.  Trying to make sure that that student has like a partner or---or a helper that---that can always assist in linking over the understanding that the teachers isn’t, uh, isn’t conveying to the student.  Uh, being more sensitive that, uh, that the---the barriers of language that are created can be overcome by these---these procedures, these strategies.  Um, --- so what happened with Carol, um, I’m sorry, with Alice, because there were two.  Al---what happened with Alice is, Alice started, uh, um, trying math nights.  And in the beginning she was having all these parents come in for math nights and she was having instruction in English.  And by just having the Spanish material available and team up parents with bilingual parents, she was able to present her English math nights and have---making sure that these parents were served.  And the parents didn’t have to have everything explained in English, they were happy that the teacher just made them a spot, uh, and got some kind of helper that could assist them in making these kind of links and they were part of it as well.  It take a lot of changes for the teacher to see that this is doable, I can make these kind of steps, and from there the teacher just took off.  She started, uh, working with another teacher that was bilingual in presenting these bilingually.  Uh, they would, uh, have, uh, math night where they, uh, Spanish speaking parents would go with the bilingual teacher and the English ones would go with her.  And then they’d switch when they would---presenting the movies so that, uh, so that the people could see them working together as a team.  And, uh---the---in fact the school is going to start using these teachers as a model to create these.  Because, again, the administrators didn’t know how to make these changes and they were still trying old methods that still didn’t work, and, um, offering workshops that it just frustrated teachers more because they weren’t creating the changes that teachers needed to see in the classrooms.  And I think teachers need to be our leaders.  Teachers are the ones that are going to create their change because teachers became teachers because they want to teach, because they care.  And a caring element is what helps these mun---connections become real connections, lifelong, lasting connections.

If---if a student, a student would be saying about his teacher that’s making these---these beginning efforts and saying, ‘I really feel like my teacher cares about my learning.  I really feel like my teacher cares that I’m understanding this.’  And they acknowledge the changes that the students make.  Again, it’s---it’s not going to directly affect immediately, but, I think the student would say that my teacher is trying, or my teacher is trying to make some kind of efforts.  I think they will be acknowledged in some way, I mean, I’ve seen that, I’ve worked with junior high students, and they know, so.  They’re going to see---label this teacher as a good teacher.  And you ask them this teacher is a good teacher, is because she’s trying to learn things to work with me.  And I think---that doesn’t go, it---uh, that doesn’t go, um, unrecognized. (door shuts)  In fact, right now, I just came from a session where you had parents that are working in the high schools as liaisons in mathematics.  And the teacher---the parents are saying that their kid, their junior high students are recognizing their efforts as well.  And there’s---they’re telling Mom, ‘you go girl, you go Mom,’ because they know that the moms are making efforts.  And with teachers, they know that these teachers are making efforts to try to---to help them better.  And they know, uh, that it’s, you know, that they know that it’s, uh, that’s---that it’s not---oh let’s just say it’s---it’s---it’s---it’s not everything that they would want but they’re acknowledging that.  And students are going to be just as appreciative of this as parents or teachers are going to be when these changes happen. 

Well, a lot of our students that---that, uh, that are working with us, the families, um, their parents don’t have more than a, say, fifth-sixth-grade education.  And when they come to the workshops and they start taking roles, um, that they’re comfortable with, in being in charge, like they are in the home, then they start feeling the self confidence that that, kind of like, um, penetrates into this---into the classrooms.  We’re seeing parents that, um, that are---that can be---that become strong leaders.  Uh, in fact, in this panel of teachers that I just came from, the, um, ---oh, sorry, this panel of parents that I just came from, it was---it was one of the most powerful sessions that I’ve ever attended at AERA.  And the reason it was powerful, because they were real stories coming from parents that have made these transformational changes that have transformed the culture of the school.  And the reason it was transformed is because they are working with teachers that were transformed that are now sharing that with the parents and letting them take some kind of lead.  And you’re seeing that reflected with the students, with the teachers, and with the parents.  So in a way it’s contagious, it affects everybody.  But, again, it’s just these beginning moves that are happening, but the kids acknowledge that, because it’s almost like they’re embraced in just a circle of just, uh, of---of---of everybody helping and sharing and it just---it just helps move these kind of things forward.  This is what moves, uh, teachers to want to---want to---want to take classes.  Um, in fact this summer I offer these classes, uh, for teachers that are going to advance their learning.  And what---what happens is, they come in and share these ideas and---and they---they---they facilitate.  I’m just a facilitator.  They share what they’ve learned, what worked for them.  And it was hard for me to just sit there and not lecture.  I had to sit there and---and do the same thing that I’m telling them to do.  And I’ve sat there and listened to them, uh, become leaders in sharing their ideas that worked in the classroom with other teachers.  And it becomes, uh, powerful, what they can do.  But the thing is, is, we’ve got to, uh, we’ve got, also, look at ourselves, university professors, and stand back and say, ‘They are the ones that know what’s needed in the classroom.’  Just like the teachers, uh, are finding out from the parents, you know, when---when can you meet?  When---when is it convenient for you to meet?  I’ll rearrange my schedule to---to, uh, to fit your schedule if you come and---and---and meet with me.  So we’re seeing all these schedules being changed because---to create this kind of connection that needs to be made, uh, in new ways.

Um, one---one of the things that I’d like to comment on is---I’m in awe---of the efforts that the teachers put out and the time and the commitment and their own money that they put out for materials and.  Uh, the reason I got involved in this is, um, I want to make it more cost effective for them.  I want to make it---if I see that the commitment---I want to make sure that---that they’re being led to a road that’s going to create the changes that they want to be create---uh, that they want to create in the classrooms.  And---and I see myself as a facilitator, as an instrument to helping them, um, to use those energies in a positive way that’s going to get them feedback so that momentum is---is continued throughout the year.  Because that’s what I feel that my research and my work is all about, is just to try to---to, uh, facilitate that enthusiasm with them, or awaken that in them and remind them why they became teachers in the first place.  And then my job becomes easy.  And that’s where I’m at now in my research, it’s---it’s easy now because they’re wanting to make these changes.  We’re walking together, just different paces, but we’re getting there.

The---the Spiral Model, what it does is---what I’ve---what I---it’s---it’s, well, I was going to say what I talked to you about earlier, but, this is going to stand alone.  The Spiral Model, what it is, is just a model that just shows the multi-dimensional learning and growing and connecting, happening with teachers, with parents, and with the students.  So it kind of looks at the dynamics of that in a---in a three dimensional figure to see how it’s all interconnected.  But to show that it’s possible to grow and change and connect and learn mathematics.  Because that’s how I would describe the Spiral Model, learning.