[SalesForce] how to pass value to page included in tab

I want to Implement functionality with one picklist for selecting object Id and several tabs presenting details of selected record. Each of tabs will have separate controller, but needs selected object id as an input. At first I thought that passing that parameter via page parameters is appropriate approach, but when I switch between the tabs, the parameter is reset. Is there any better way to do that, or am I missing something in my code? Below I enclose simplified code:

Parent page for selecting object id

<apex:page standardStylesheets="false" sidebar="false" showHeader="false" controller="testParentCtr">
  <apex:form >
      <apex:selectList value="{!param}" size="1" >
          <apex:selectOption itemLabel="1" itemValue="1" />
          <apex:selectOption itemLabel="2" itemValue="2" ></apex:selectOption>
          <apex:selectOption itemLabel="3" itemValue="3" ></apex:selectOption>      
      </apex:selectList>  
      <apex:commandButton rerender="tabpanel"  value="Set"/>
  </apex:form>

  <br/> 
  Parent Page->CurrentPage.parameters.param: {!$CurrentPage.parameters.param}
  <br/>
  ApexPages.currentPage().getParameters().get('param'): {!param}

        <apex:tabPanel switchType="server" id="tabpanel">
            <apex:tab label="child1"><apex:include pageName="child" /></apex:tab>
            <apex:tab label="child2"><apex:include pageName="child" /></apex:tab>
        </apex:tabPanel>   

</apex:page>

and it's controller

public with sharing class testParentCtr {

    public String param{
        get;
        set{ 
            ApexPages.currentPage().getParameters().put('param', value ); //hope this will propagate 'param' new value to child page
            param=value; 
           } 
        }

   public testParentCtr(){
       this.param =  ApexPages.currentPage().getParameters().get('param'); //just bind to param to set default value on selectList
   }

}

Plus the child page (included in tabs)

<apex:page controller="testChildCtr" standardStylesheets="false" sidebar="false" showHeader="false">

  Child->CurrentPage.parameters.param:{!$CurrentPage.parameters.param}
  <br/>
  Child->ApexPages.currentPage().getParameters().get('param') :{!param}

</apex:page>

and it's controller.

public with sharing class testChildCtr {

public String getParam(){
    return ApexPages.currentPage().getParameters().get('param'); 
}

}

Thank You for advise.